ALGEBRA II HONORS - (0.1-0.4 Quiz)
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Questions and Answers

What is a function?

A relation in which every input has exactly one output.

What is domain?

The set of all possible inputs for a function

What is range?

The set of all possible outputs for a function.

An open circle includes the point.

<p>False</p> Signup and view all the answers

A closed circle includes the point

<p>True</p> Signup and view all the answers

What does the () mean in interval notation?

<p>Non inclusive</p> Signup and view all the answers

What does the [] mean in interval notation?

<p>Inclusive</p> Signup and view all the answers

What does the U mean in interval notation?

<p>Union (combine sets)</p> Signup and view all the answers

Is this equation in interval or inequality notation? - (2,4)U[7,9)

<p>Interval</p> Signup and view all the answers

When using interval notation you always write your answers from _____ to ________.

<p>least, greatest</p> Signup and view all the answers

Linear functions must be ______.

<p>tilitrd</p> Signup and view all the answers

Match the formula to its form

<h1>Point slope form = y-y1 = m(x-x1) Slope intercept form = y = mx+b Standard form = Ax+By=C</h1> Signup and view all the answers

When is point slope form best to use?

<p>When given a point and a slope</p> Signup and view all the answers

When is slope intercept form best to use?

<p>When given slope and y-intercept</p> Signup and view all the answers

When is standard form best to use?

<p>When given intercepts</p> Signup and view all the answers

How would you rearrange the equation 3x + 5y = 10 to solve for y?

<p>y = -\frac{3}{5}x + 2</p> Signup and view all the answers

Identify the slope and y-intercept of the line given by the equation y = -1/3x - 6.

<p>Slope is -1/3, y-intercept is -6.</p> Signup and view all the answers

What is the standard form of the equation for the line with slope -2 passing through the point (-4, -1)?

<p>2x + y = -9</p> Signup and view all the answers

For the equation y - 6 = -(x + 2), identify the slope and the point it passes through.

<p>Slope is -1, point is (-2, 6).</p> Signup and view all the answers

What is the relationship between the equations y = -4 and 3x + 5y = 10 when graphed?

<p>The line <code>y = -4</code> is horizontal, and it intersects <code>3x + 5y = 10</code> at the point where y equals -4.</p> Signup and view all the answers

What is the slope of the line that passes through the points (-1,4) and (1,6)?

<p>The slope is 1.</p> Signup and view all the answers

Write the equation of a line with an x-intercept of 3 and a y-intercept of -2.

<p>The equation is $y = \frac{2}{3}x - 2$.</p> Signup and view all the answers

What is the equation of the line with a slope of 2 that passes through the point (2,7)?

<p>The equation is $y = 2x + 3$.</p> Signup and view all the answers

Determine the slope and y-intercept of the line with the equation $6y + 10 = 3x$.

<p>The slope is $\frac{1}{2}$ and the y-intercept is $\frac{5}{3}$.</p> Signup and view all the answers

Create the equation of a line that has the slope of the line $6y + 10 = 3x$ and the y-intercept of 4.

<p>The equation is $y = \frac{1}{2}x + 4$.</p> Signup and view all the answers

Find the domain and range of the following graph using interval notation.

<p>D: (−&amp;,−2]U[1,2]U[2,&amp;), R: [-&amp;,0]U[2]U[3]</p> Signup and view all the answers

Convert (-2,3] from interval notation to inequality notation

<p>-2&lt;x&lt;_3</p> Signup and view all the answers

Find the domain and range using interval notation.

<p>D: (-2,3], R: [3,12]</p> Signup and view all the answers

Find the domain and range using interval notation.

<p>D: (-&amp;,-5]U(-2,&amp;), R: (-&amp;,-2]U(1,&amp;)</p> Signup and view all the answers

Follow the image.

<p>Answers vary</p> Signup and view all the answers

Point slope form:

<p>y-3=-2/3(x+3)</p> Signup and view all the answers

Slope intercept form

<p>y=-2/3x+1</p> Signup and view all the answers

Standard form (A = reciprocal of x-intercept, vice versa)

<p>2x+3y=3</p> Signup and view all the answers

Convert y=-5x+21 into standard form.

<p>5x+y=21</p> Signup and view all the answers

Write the particular equation of the line that contains (3,7) and has a slope of 11.

<p>y-7=11(x-3)</p> Signup and view all the answers

Convert y-7=11(x-3) into standard form.

<p>-11x+y=-26</p> Signup and view all the answers

write the particular equation of the line that contains (-2,-3) and has a slope of 3/5

<p>y+3=3/5(x+2)</p> Signup and view all the answers

Find domain and range using interval notation

<p>D: [-1,&amp;), R: [-2,2]</p> Signup and view all the answers

Describe the equation of parallel lines.

<p>Same m, different b</p> Signup and view all the answers

Describe the equation of perpendicular lines

<p>Opposite slopes</p> Signup and view all the answers

What is a perpendicular bisector?

<p>A line that bisects a line segment at its midpoint.</p> Signup and view all the answers

What is the perpendicular bisector formula?

<p>x1-x2/2, y1-y2/2</p> Signup and view all the answers

Write the particular equation of the line that contains (4,1) and is perpendicular to the graph of 5x-7y=44

<p>y-1=-7/5(x-4)</p> Signup and view all the answers

What is the value of A that would make the lines 6x-8y=11 and Ax+4y=11 parallel?

<p>A=-3</p> Signup and view all the answers

Find the value of k so that 6y=kx+10 and 1/5y=1/10x-2 are parallel

<p>k=3</p> Signup and view all the answers

Find the value of A so that would make the lines 4x-3y=10 and Ax+4y=7 perpendicular.

<p>A=3</p> Signup and view all the answers

Write an equation of the perpendicular bisector of the segment that joins the point (4,-8) and (10,12)

<p>y-2=-3/10(x-7)</p> Signup and view all the answers

Study Notes

Lines and Slopes

  • To find the equation of a line passing through two points, use the slope formula ( m = \frac{y_2 - y_1}{x_2 - x_1} ).
  • The points (-1, 4) and (1, 6) give a slope of ( m = \frac{6 - 4}{1 - (-1)} = \frac{2}{2} = 1 ).
  • The equation can be expressed in point-slope form: ( y - y_1 = m(x - x_1) ), leading to ( y - 4 = 1(x + 1) ) or simplified to ( y = x + 5 ).

x-intercept and y-intercept

  • A line's x-intercept is where it crosses the x-axis (y=0); the given x-intercept is 3, so the point is (3,0).
  • A line's y-intercept is where it crosses the y-axis (x=0); the given y-intercept is -2, so the point is (0,-2).
  • Using intercepts, the line can be expressed with the intercept form: ( \frac{x}{3} + \frac{y}{-2} = 1 ), or simplified to ( 2x + 3y = 6 ).

Point-Slope Form

  • A line with a slope of 2 and passing through (2, 7) can be derived from the point-slope formula.
  • The slope is defined as ( m = 2 ) and the line equation is ( y - 7 = 2(x - 2) ).
  • Simplifying results in the equation: ( y = 2x + 3 ).

Honors Problem

  • The equation ( 6y + 10 = 3x ) can be rearranged to find its slope and y-intercept.
  • Rearranging gives standard form ( y = \frac{1}{2}x - \frac{5}{3} ); thus, the slope is ( \frac{1}{2} ) and the y-intercept is ( -\frac{5}{3} ).
  • Creating a new line requires maintaining the same slope ( \frac{1}{2} ) but changing the y-intercept to 4: the new line equation is ( y = \frac{1}{2}x + 4 ).

Graph Analysis of Line Segments

  • The line has two marked points: (-2, 2) and (2, 0).
  • The line extends indefinitely to the left due to an arrow at the end.
  • The line continues indefinitely to the right, also indicated by an arrow.

Domain and Range

  • Domain: Represents all possible x-values of the line, expressed in interval notation as (−∞,1)∪[2,∞)(-\infty, 1) \cup [2, \infty)(−∞,1)∪[2,∞).

    • Includes all x-values less than 1, and all x-values from 2 onward.
    • The interval notation indicates that 1 is excluded while 2 is included.

  • Range: Represents all possible y-values of the line, which is noted as (−∞,0]∪∪(-\infty, 0] \cup \cup(−∞,0]∪∪ (incomplete).

    • Includes all y-values up to 0; specific upper limit needs clarification.
    • Indicates that the value of y cannot exceed 0.

Important Considerations

  • The inclusion of arrows signifies that the line continues past the marked points.
  • Interval notation is essential in determining boundaries and the nature of inclusivity/exclusivity of endpoints.

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