Foundations and Pre-Calculus 10 Unit 5 Homework Package PDF

**Foundations and Pre-Calculus 10** **Unit 5 Homework Package: Graphing and Systems of Linear Equations** +-----------------------------------+-----------------------------------+ | **[Day 1: Functions and | 5\. Which sets of ordered pairs | | Relations]** | represent function...

**Foundations and Pre-Calculus 10** **Unit 5 Homework Package: Graphing and Systems of Linear Equations** +-----------------------------------+-----------------------------------+ | **[Day 1: Functions and | 5\. Which sets of ordered pairs | | Relations]** | represent functions? Identify | | | the **domain and range** of | | 1\. For a word game, words that | each set of ordered pairs. | | begin with the letter Z can be | | | difficult to find. | a) | | | [{(1,3) , (2,6), (3,9), (4, 12)}] | | a\) What does this arrow diagram | {.math | | represent? |.inline} | | | | | b\) Represent this relation in | b) | | two different ways. | [{(1, 0), (0,1), (−1,0), (0,−1)}] | | | {.math | |  | c) | | | [{(2,3), (4,5), (6,7), (8,9)}]{.m | | 2\. A digital clock displays | ath | | digits from 0 to 9 by lighting |.inline} | | up different segments in two | | | squares. For example, the digit | d) | | 2 needs 5 segments to light up, | [{(0,1), (0,2), (1,2), (0,3), (1, | | as shown. | 3), (2,3)}]{.math | | |.inline} | | a\) List the set of ordered | | | pairs of the form: (digit, | 6\. Write in function notation | | number of segments lit up) | | | | a\) [*C* = 20*n* + 8]{.math | | b\) Represent this relation in |.inline} c) [*t* = 5*d*]{.math | | two different ways. |.inline} | | | | | 3\. The association "is the | b\) [*P* = *n* − 3]{.math | | parent of" is shown in the |.inline} d) [*y*=  − *x*]{.math | | diagram. Each dot represents a |.inline} | | person, and each arrow maps a | | | parent to their child. | 7\. Which statement is true? | | | Give an example to justify your | | a\) How many children are shown? | choice. | | | | | b\) How many parents are shown? | a\) All functions are relations, | | | but not all relations are | | c\) How many grandparents are | functions. | | shown? | | | | b\) All relations are functions, | | Justify your answers. | but not all functions are | | | relations. | | Chart, line chart Description | | | automatically generated | 8\. In Scrabble, each letter is | | | worth a certain number of | | 4\. Which arrow diagrams | points. Here are some letters | | represent functions? | and their points. | | | | | a\) b) | associate these letters and | | Diagram Description | their points | | automatically generated | | | | b\) which table in part a | | c\)  | | | | 9\. For the function | | | [*f*(*x*) =  − 5*x* + 11,]{.math | | |.inline} determine: | | | | | | a\) [*f*(1)]{.math.inline} c) | | | [*f*(0)]{.math.inline} | | | | | | b\) [*f*(−3)]{.math.inline} d) | | | [*f*(1.2)]{.math.inline} | | | | | | 10\. a) For the function | | | [*f*(*n*) = 2*n* − 7]{.math | | |.inline}, determine *n* when: | | | | | | i\) [*f*(*n*) = 11]{.math | | |.inline} ii) | | | [*f*(*n*)=  − 6]{.math.inline} | | | | | | b\) For the function | | | [*g*(*x*)=  − 5*x* + 1]{.math | | |.inline}, determine *x* when: | | | | | | i\) [*g*(*x*) = 41]{.math | | |.inline} ii) | | | [*g*(*x*) =  − 16]{.math | | |.inline} | | | | | | 11\. The lengths of the sides of | | | a triangle, in units, are | | | [*s*, *s* + 5,]{.math.inline} | | | and [*t*]{.math.inline}*.* Its | | | perimeter is 16 units. Use | | | function notation to express | | | *t* as a function of *s*. What | | | are the domain and range of the | | | function? | +===================================+===================================+ | **[DAY 2: Domain and | 5\. Which of these graphs | | Range]** | represent a function? Justify | | | your answer (5.5 -- 8) | | 1\. List the domain and range of | | | the graph of each function | a\) Chart, line chart | | | Description automatically | | a\)  | | generated](media/image8.png)b) | | | Chart, scatter chart | c\) Chart, line chart | | Description automatically | Description automatically | | generated | generated d)  | | generated](media/image10.png) | | | | e) | | 2\. How can you tell each graph | | | in the previous question | 6\. Determine the rdomain and | | represent functions? | range of the graph of each | | | function. | | 3\. Which of these graphs | | | represent a function? Justify | a\)  | | a\) A picture containing text, | b) Chart, line chart | | shoji, crossword puzzle | Description automatically | | Description automatically | generated | | generatedb) | | |  | c\) d) | | function to its domain and | | | range listed below | 7\. Answer the following | | | questions about the given | | i\) domain: [1 ≤ *x* ≤ 3;]{.math | graph: | |.inline} range: | | | [2 ≤ *y* ≤ 4]{.math.inline} | a\) is this a function? | | | | | ii\) domain: | b\) find [*f*( − 1)]{.math | | [1 ≤ *x* ≤ 3;]{.math.inline} |.inline} | | range: [1 ≤ *y* ≤ 4]{.math | | |.inline} | c\) find [*f*(2)]{.math.inline} | | | | | iii\) domain: [0 ≤ *x*;]{.math | d\) find [*f*(4)]{.math.inline} | |.inline} range: [*y* = 2]{.math | | |.inline} | e\) state the domain and range | | | for this function | | iv\) domain: | | | [1 ≤ *x* ≤ 4;]{.math.inline} | 9\. Use the graphs of f(x) and | | range: [1 ≤ *y* ≤ 2]{.math | g(x) to evaluate the following: | |.inline} | | | | a\) [*f*(2) − *g*(2)]{.math | | a\) Chart, line chart |.inline} | | Description automatically | | | generated b) | b\) [*f*(4) − *g*(4)]{.math | |  |.inline} | | | | | c\) Chart, line chart | c) [\$\\frac{f(0)}{g(3)}\$]{.math | | Description automatically |.inline} | | generated d) ![A picture | | | containing text, shoji, clock | d\) [*f*(*g*(5))]{.math.inline} | | Description automatically | -\> this is f of g of 5. Find g | | generated](media/image16.png) | of 5 first, then find f of that | | | value. | | 8\. Answer the following | | | questions about the given | 10\. If the graph of f(x) is | | graph: | given, find: | | | | | a\) explain why this graph | a\) [*f*( − 1)]{.math.inline} | | represents a function | | | | b\) [*f*(0)]{.math.inline} | | b\) find [*f*( − 1)]{.math | | |.inline}) | c\) [*f*(6)]{.math.inline} | | | | | c\) find [*f*(3)]{.math | d\) x if [*f*(*x*) = 0]{.math | |.inline}\ |.inline} | | d) find [*f*(4)]{.math.inline} | | | | | | e\) state the domain and range | | | for this function | | +-----------------------------------+-----------------------------------+ | **[DAY 3: Interpreting Data and | 3\. Sketch a graph of each | | Graphing Linear | linear function. | | Equations]** | | | | a\) [*f*(*x*) = 4*x* + 3]{.math | | 1\. Which graphs represent |.inline} b) | | linear relations? How do you | [*g*(*x*)=  − 3*x* + 5]{.math | | know? |.inline} | | | | | a)![Chart, line chart Description | c\) [*h*(*x*) = 9*x* − 2]{.math | | automatically |.inline} d) | | generated](media/image30.png) b) | [*k*(*x*)=  − 5*x* − 2]{.math | | Chart, line chart Description |.inline} | | automatically generated | | | | 4\. What is the slope of... | | c) d) | 5\$]{.math.inline} | | Chart, line chart Description | | | automatically generated | b\) [5*x* − 2*y* + 7 = 1]{.math | | |.inline} | | 2\. Create a table of values | | | when necessary, then graph each | c) | | relation | [*x*^2^ + 6(*y*−5) = (*x*+3)^2^]{ | | |.math | | b\) which equations in part a |.inline} | | represent linear relations? | | | | 5\. Find the x and y-intercepts | | i\) [*y* = 2*x* + 8]{.math | for | |.inline} ii) | | | [*y* = 0.5*x* + 12]{.math | a\) [3*x* + 7*y* = 42]{.math | |.inline} |.inline} | | | | | iii\) [*y* = *x*^2^ + 8]{.math | b\) [\$\\frac{2}{3}x - | |.inline} iv) [*y* = 2*x*]{.math | \\frac{3}{4}y = 2\\ \$]{.math | |.inline} |.inline} | | | | | v\) [*x* = 7]{.math.inline} vi) | 6\. Sketch the graph of each of | | [*x* + *y* = 6]{.math.inline} | the following. Do not use a | | | table of values. Do not use any | | | fractional points. Also find | | | the coordinates of their x and | | | y-intercepts, and their domain | | | and range. | | | | | | a\) [*y* = 2*x* − 1]{.math | | |.inline} | | | | | | b\) [\$y + 4 = | | | \\frac{3}{2}\\left( x - 1 | | | \\right)\$]{.math.inline} | | | | | | c\) [5*x* + 2*y* + 4 = 0]{.math | | |.inline} | | | | | | d\) [\$y = \\frac{5}{3}x - | | | 2\$]{.math.inline} | | | | | | e\) [\$y - 2 = - | | | \\frac{3}{4}\\left( x - 3 | | | \\right)\$]{.math.inline} | +-----------------------------------+-----------------------------------+ | **[DAY 4: Midpoint, Distance, | 5\. A trench is to be dug to lay | | Slope, and Lines]** | a drainage pipe. To ensure that | | | the water in the pipe flows | | 1\. For each line segment, is | away, the trench must be dug so | | its slope positive, negative, | that it drops 1 in. for every 4 | | zero, or not defined? | ft. measured horizontally. | | | | | a\) b) | | | Chart, line chart Description | b\) Suppose the trench drops | | automatically generated | [\$6\\frac{1}{2}\$]{.math | | |.inline} in. from beginning to | | c\) d) | | | A picture containing shoji | c\) Suppose the trench is 18 ft. | | Description automatically | long measured horizontally. By | | generated | how much does it drop over that | | | distance? | | 2\. For each line segment, | | | determine its rise, run, and | 6\. Match each line below with a | | slope. | slope. Explain your choices. | | | | | a\) ![Chart, line chart | a\) slope: [ − 2]{.math.inline} | | Description automatically | | | generated](media/image38.png)b) | b\) slope: | | Chart, line chart Description | [\$\\frac{1}{2}\$]{.math | | automatically generated |.inline} | | | | | c\) ![Chart, line chart | c\) slope: [\$- | | Description automatically | \\frac{1}{2}\$]{.math.inline} | | generated](media/image40.png)d) | | | Chart, line chart Description | d\) slope: {.math.inline} | | automatically generated | | | | 7\. For each of the following | | 3\. a) Chose two points on line | pairs of points, find the (1) | | segment DE. Use these points to | midpoint (2) slope (3) distance | | determine the slope of the line | between them: | | segment. | | | | a\) [(3,1) & (9, 9)]{.math | | b) Choose |.inline} | | two different points on segment | | | DE and calculate its slope. | b\) [(−2,4) & (7,  − 1)]{.math | | |.inline} | | c\) Compare the slopes you | | | calculated in parts a and b. | c\) [(−5,−2) & (10, 6)]{.math | | Explain the result. Why does |.inline} | | this happen? | | | | 8\. The coordinates of the | | 4\. a) Determine the slope of | endpoints of a line segments | | the line that passes through | are given. Find the coordinates | | each pair of points. | of three points that divide | | | each segment into four equal | | b\) Explain what each slope | parts: | | tells you about the line. | | | | a\) A(-6,4), B(10, -4) | | i\) P(1,2) and Q(3,6) | | | | b\) C(2,9), D(-14,-3) | | ii\) S(0,1) and T(8,5) | | | | 9\. The coordinates of the | | iii\) V(-1,4) and R(3, -8) | endpoints of a line segment are | | | given. Find the coordinates of | | iv\) U(-12, -7) and W(-6, -5) | two points that divide each | | | segment into three equal parts: | | | | | | a\) A(-8, 5), B(10, -4) | | | | | | b\) C(-4, -9), D(-14, -3) | | | | | | 10\. If M is the midpoint of A & | | | B, and the coordinates of A & M | | | are given below, find the | | | coordinates of the point B: | | | | | | a\) A(-2, 4), M(3, 1) | | | | | | b\) A(-5, -2), M(6, 3) | | | | | | 11\. Sketch the graphs of the | | | lines with the following slopes | | | and points: | | | | | | a\) m = 5 ; P = (-2, 1) | | | | | | b\) m = [\$\\frac{1}{2}\$]{.math | | |.inline} ; P =(4, 2) | | | | | | c\) m = [\$- | | | \\frac{5}{3}\$]{.math.inline} | | | ; P = (6, -1) | +-----------------------------------+-----------------------------------+ | **[DAY 5: Perpendicular and | 9\. What is the slope of the | | Parallel Lines]** | line parallel to | | | [6*x* + 2*y* = 5?]{.math | | 1\. For each grid below: |.inline} | | | | | i\) write the coordinates of the | 10\. What is the slope of the | | 2 labelled points on each line. | line perpendicular to | | | [5*x* − 2*y* = 5?]{.math | | ii\) are the two lines parallel, |.inline} | | perpendicular, or neither? | | | Justify your answer. | 11\. If the line | | | [4*x* + 3*y* = 8]{.math | | a\)  | [(4*a*+1, 4*a*−2)]{.math | | b) Chart, line chart |.inline} and | | Description automatically | [3 − *a*, 7*a* − 2)]{.math | | generated |.inline}, find the value of | | | [*a*]{.math.inline}. | | c\)  | Slope-intercept | | d) Chart, line chart | forms]** | | Description automatically | | | generated | 1\. For each equation, identify | | | the slope and y-intercept of | | 2\. The coordinates of the | its graph | | endpoints of segments are given | | | below. Are the two line | a\) [*y* = 4*x* − 7]{.math | | segments parallel, |.inline} b) | | perpendicular, or neither? | [*y* = *x* + 12]{.math.inline} | | Justify your answer. | | | | c\) [\$y = - \\frac{4}{9}x + | | a) [*S*(−4,−1),  *T*(−1,5)]{.math | 7\$]{.math.inline} d) [\$y = | |.inline} and | 11x - \\frac{3}{8}\$]{.math | | [*U*(1,1),  *V*(5,−1)]{.math |.inline} | |.inline} | | | | e\) [\$y = | | b) [*B*(−6,−2),  *C*(−3,3)]{.math | \\frac{1}{5}x\$]{.math.inline} | |.inline} and | f) [*y* = 3]{.math.inline} | | [*D*(2,0),  *E*(5,5)]{.math | | |.inline} | 2\. Write an equation for the | | | graph of a linear function | | c) [*N*(−6,2),  *P*(−3,−4)]{.math | that: | |.inline} and | | | [*Q*(1, −3),  *R*(3,4)]{.math | a\) has a slope 7 and | |.inline} | y-intercept 16 | | | | | d\) [*G*(−2,5),  *H*(4,1)]{.math | b\) has slope [\$- | |.inline} and | \\frac{3}{8}\$]{.math.inline} | | [*J*(1, −4),  *K*(7,0)]{.math | and y-intercept 5 | |.inline} | | | | c\) passes through | | 3.A line passes through | [*H*(0,  − 3)]{.math.inline} | | [*A*(5,−2)]{.math.inline} and | and has slope | | [*B*(3, 2)]{.math.inline}. | [\$\\frac{7}{16}\$]{.math | | |.inline} | | a\) Draw line AB on a grid and | | | determine its slope | d\) has y-intercept [ − 8]{.math | | |.inline} and slope [\$- | | b\) Line CD is parallel to AB, | \\frac{6}{5}\$]{.math.inline} | | what is the slope of CD? | | | | e\) passes through the origin | | c\) Given that | and has slope [\$- | | [  *Q*(1,  − 4)]{.math.inline} | \\frac{5}{12}\$]{.math.inline} | | lies on CD, draw line CD. | | | Determine the coordinates of | 3\. Graph each equation. | | its x- and y-intercepts. | | | | a\) [*y* = 2*x* − 7]{.math | | d\) Line EF is perpendicular to |.inline} b) | | AB. What is the slope of EF? | [*y* =  − *x* + 3]{.math | | |.inline} | | e\) Given that [ R(−4,−4)]{.math | | |.inline} lies on EF, draw line | c\) [\$y = - \\frac{1}{4}x + | | EF. Determine the coordinates | 5\$]{.math.inline} d) [\$y = | | of its x- and y-intercepts. | \\frac{5}{2}x - 4\$]{.math | | |.inline} | | 4\. The coordinates of the | | | vertices of [*ΔDEF*]{.math | e) [*V* =  − 100*t* + 6000]{.math | |.inline} are |.inline} f) | | [*D*(−3,−2),  *E*(1,4)]{.math | [*C* = 10*n* + 95]{.math.inline} | |.inline} and [*F*(4,2)]{.math | | |.inline}. Is [*ΔDEF*]{.math | 4\. For a service call, an | |.inline} a right triangle? | electrician charges an \$80 | | Justify your answer. (6.2 -- | initial fee, plus \$50 for each | | 17) | hour she works. | | | | | 5\. Determine the value of *c* | a\) Write an equation to | | so that the line segment with | represent the total cost, C | | endpoints [*B*(2, 2)]{.math | dollars , for t hours of work | |.inline} and [*C*(9, 6)]{.math | | |.inline} is parallel to the | b\) How would the equation | | line segment with endpoints | change if the electrician | | [*D*(*c*,  − 7)]{.math.inline} | charges \$100 initial fee plus | | and [*E*(5,  − 3)]{.math | \$40 for each hour she works? | |.inline}. | | | | 5\. The total fee for | | 6\. Find the slope of the line | withdrawing money at an ATM in | | that is perpendicular to the | a foreign is a \$3.50 foreign | | line that passes through (4, | cash withdrawal fee, plus a 2% | | -2) and (-5, 8) | currency conversion fee. Write | | | an equation to represent the | | 7\. If the slopes of two | total fee, *F* dollars, for | | parallel lines are | withdrawing *d* dollars. ( | | [*m*~1~ = *x* − 2]{.math | | |.inline} and |  | | | | | [*m*~2~ = 5*x* − 3]{.math | 6\. A student said that the | |.inline}, find the value of | equation of this graph is | | [*x*]{.math.inline} | [*y* =  − 3*x* + 4]{.math | | |.inline} | | 8\. If the slopes of two | | | perpendicular lines are | a\) What mistake did the student | | [*m*~1~ = *x* + 1]{.math | make? | |.inline} and | | | [*m*~2~ = 6*x* + 1]{.math | b\) What is the equation of the | |.inline}, find the value of | graph? | | [*x*]{.math.inline} | | | | 10\. Find the equation of the | | **[Day 6 (cont'd)]** | line in slope-intercept form: | | | | | 7\. For each graph that follows: | a\) slope = [\$- | | | \\frac{1}{4}\$]{.math.inline}; | | i\) Determine its slope and | passes through the point (4, | | y-intercept. | -2) | | | | | Ii) Write an equation to describe | b\) passes through the points | | the graph, then verify the | (1, 6) and (-2, -9) | | equation. | | | | c\) passes through the points | | iii\) Use the equation to | (8, 6) and (-4, 2) | | calculate the value of y when x | | | = 10. | 11\. Find the equation of the | | | line in point-slope form: | | a\) b) | b\) has a slope of | | Chart, line chart Description | [\$\\frac{7}{3}\$]{.math | | automatically generated |.inline}and passes through the | | | point (3, 11) | | c\) d) | through the point (1, 6) | | A graph with numbers and | | | letters Description | **[DAY 7: Standard and General | | automatically generated with | Form]** | | low confidence | | | | 1\. In which form is each | | 8. | equation written? (6.6 -- 4) | | | | | a\) For each line, write an | a\) [8*x* − 3*y* = 52]{.math | | equation in slope-point form. |.inline} b) | | | [9*x* + 4*y* + 21 = 0]{.math | | b\) Write each equation in part |.inline} | | (a) in slope-intercept form, | | | then determine the x and | c\) [*y* = 4*x* + 7]{.math | | y-intercepts of each graph. |.inline} d) | | | [*y* − 3 = 5(*x*+7)]{.math | | i\) ii) | 2\. Determine the x and | | Chart, line chart Description | y-intercepts for the graph of | | automatically generatediii) | each equation. (6.6 -- 5) | | ![Chart, line chart Description | | | automatically | a\) [8*x* − 3*y* = 24]{.math | | generated](media/image54.png)iv) |.inline} b) | | Chart, line chart Description | [7*x* + 8*y* = 56]{.math | | automatically generated |.inline} | | | | | 9\. Write an equation for the | c\) [4*x* − 11*y* − 88]{.math | | line that passes through each |.inline} d) | | pair of points. Write each | [2*x* − 9*y* = 27]{.math | | equation in slope-point form |.inline} | | and in slope-intercept form. | | | | 3\. Write each equation in | | a\) [*B*(−2,−5)]{.math.inline} | general form (6.6 -- 6) | | and [*C*(1,1)]{.math.inline} | | | | a\) [4*x* + 3*y* = 36]{.math | | b\) [*Q*(−4,7)]{.math.inline} |.inline} b) | | and [*R*(5,  − 2)]{.math | [2*x* − *y* = 7]{.math.inline} | |.inline} | | | | c\) [*y* =  − 2*x* + 6]{.math | | c\) [*U*( − 3,  − 7)]{.math |.inline} d) | |.inline} and [*V*(2, 8)]{.math | [*y* = 5*x* − 1]{.math.inline} | |.inline} | | | | 4\. Write each equation in | | d\) [*H*( − 7,  − 1)]{.math | slope-intercept form (6.6 -- | |.inline} and | 12) | | [*J*( − 5,  − 5)]{.math | | |.inline} | a\) [4*x* + 3*y* − 24 = 0]{.math | | |.inline} b) | | | [3*x* − 8*y* + 12 = 0]{.math | | |.inline} | | | | | | c\) [2*x* − 5*y* − 15 = 0]{.math | | |.inline} d) | | | [7*x* + 3*y* + 10 = 0]{.math | | |.inline} | | | | | | 5\. Determine the slope of the | | | line with each equation. (6.6 | | | -- 13) | | | | | | a\) [4*x* + *y* − 10 = 0]{.math | | |.inline} b) | | | [3*x* − *y* + 33 = 0]{.math | | |.inline} | | | | | | c\) [5*x* − *y* + 45 = 0]{.math | | |.inline} d) | | | [10*x* + 2*y* − 16 = 0]{.math | | |.inline} | | | | | | 6\. Graph each equation. (6.6 -- | | | 14) | | | | | | a\) [*x* − 2*y* + 10 = 0]{.math | | |.inline} b) | | | [2*x* + 3*y* − 15 = 0]{.math | | |.inline} | | | | | | c\) [7*x* + 4*y* + 4 = 0]{.math | | |.inline} d) | | | [6*x* − 10*y* + 15 = 0]{.math | | |.inline} | | | | | | 7\. Which equations below are | | | equivalent? (6.6 -- 24) | | | | | | a\) [*y* = 3*x* + 6]{.math | | |.inline} b) | | | [2*x* − 3*y* − 3 = 0]{.math | | |.inline} | | | | | | c\) [\$y - 2 = | | | \\frac{2}{3}\\left( x - 2 | | | \\right)\$]{.math.inline} d) | | | [3*x* − *y* − 6 = 0]{.math | | |.inline} | | | | | | e\) [\$y = \\frac{2}{3}x - | | | 1\$]{.math.inline} f) | | | [*y* − 3 = 3(*x*−3)]{.math | | |.inline} | | | | | | g\) [\$y - 1 = | | | \\frac{2}{3}\\left( x - 3 | | | \\right)\$]{.math.inline} h) | | | [*y* + 3 = 3(*x* − 1)]{.math | | |.inline} | | | | | | 8\. If an equation of a line | | | cannot be written in general | | | form, the equation does not | | | represent a linear function. | | | Write each equation in general | | | form, if possible. Indicate | | | whether each equation | | | represents a linear function | | | (6.6 -- 26) | | | | | | a\) [\$\\frac{x}{4} + | | | \\frac{y}{3} = 1\$]{.math | | |.inline} b) [\$y = | | | \\frac{10}{x}\$]{.math.inline} | | | | | | c\) [*y* = 2*x*(*x*+4)]{.math | | |.inline} d) [\$y = \\frac{x + | | | y}{4} + 2\$]{.math.inline} | +-----------------------------------+-----------------------------------+ | **[DAY 8: The | **[DAY 9: The | | circle]** | Ellipse]** | | | | | 1\. Graph each of the following | 1\. Graph each of the following. | | (not all are circles) | | | | a\) [\$\\frac{\\left( x - 2 | | a\) [\$y = - \\frac{2}{3}x + | \\right)\^{2}}{9} + | | 4\$]{.math.inline} | \\frac{\\left( y + 1 | | | \\right)\^{2}}{4} = 1\\ | | b\) [*x* + *y* = 2]{.math | \$]{.math.inline} | |.inline} | | | | b\) [\$\\frac{\\left( x + 3 | | c\) [*x*^2^ + *y*^2^ = 4]{.math | \\right)\^{2}}{4} + y\^{2} = | |.inline} | 1\$]{.math.inline} | | | | | d) | c\) [\$\\frac{\\left( x - 3 | | [(*x*+3)^2^ + (*y*−1)^2^ = 9]{.ma | \\right)\^{2}}{4} + | | th | \\frac{\\left( y + 1 | |.inline} | \\right)\^{2}}{9} = 1\$]{.math | | |.inline} | | e) | | | [(*x*−2)^2^ + (*y*+4)^2^ = 4]{.ma | d\) [\$\\left( x - 1 | | th | \\right)\^{2} + \\frac{\\left( | |.inline} | y - 2 \\right)\^{2}}{9} = | | | 4\$]{.math.inline} | | f) | | | [*x*^2^ + (*y*−2)^2^ = 16]{.math | 2\. Find the domain and range | |.inline} | for each of the graphs in | | | question 1 | | g\) [*x* = 3]{.math.inline} | | | | 3\. What is the exact length of | | h\) [*y* =  − 2]{.math.inline} | the major axis for | | | | | 2\. Find the domain and range | [\$\\frac{\\left( x - 2 | | for each of the graphs in | \\right)\^{2}}{9} + | | question 1 | \\frac{\\left( y + 1 | | | \\right)\^{2}}{4} = 1\\ \$]{.math | | 3\. What is the equation of each |.inline} | | of the following circles? | | | | 4\. Find the exact length of the | | a\) Diagram Description | minor axis for | | automatically generated | | | | [\$\\frac{\\left( x + 1 | | b\)  | \\right)\^{2}}{25} = 1\$]{.math | | |.inline} | | 4\. Find the equation of a | | | circle with a centre at | 5\. Find the equation of each of | | [( − 2, 5)]{.math.inline} and | the following graphs: | | which passes through the point | | | [(1,−1).]{.math.inline} | a\) Diagram Description | | | automatically generated | | 5\. Sketch the graph of | | | [(*x*+1)^2^ + (*y*−2)^2^ = 9]{.ma | b\) ![Diagram Description | | th | automatically | |.inline} for [*y* ≥ 2]{.math | generated](media/image60.png) | |.inline} | | | | 6\. Sketch the graph of | | 6\. Sketch the graph of | [\$\\frac{\\left( x - 1 | | [(*x*+1)^2^ + (*y*−2)^2^ = 9]{.ma | \\right)\^{2}}{25} + | | th | \\frac{\\left( y + 3 | |.inline} for | \\right)\^{2}}{4} = 1\$]{.math | | [ − 3 ≤ *x* ≤  − 1]{.math |.inline} for | |.inline} | [ − 1 ≤ *x* ≤ 4]{.math.inline} | +-----------------------------------+-----------------------------------+ | **[DAY 10: | **[DAY 11: Systems of | | Inequalities]** | Inequalities and Piecewise | | | Functions]** | | 1\. Express each solution on the | | | number line: | 1\. Graph each of the following: | | | | | a\) [*x* \> 3]{.math.inline} | a\) A black and white math | | | equation Description | | b\) [*x* \ 6x\\left( | | | x - 2 \\right)\$]{.math | | |.inline} | | | | | | 3\. Graph each of the following: | | | | | | a\) [*y* \ \\ - | | | \\frac{3}{5}(x - 2)\$]{.math | | |.inline} | | | | | | d\) [*x* \