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The number of people, f(x), at a tourist destination is a function of time, in months. Using the graph of f(x), find f(4).
The number of people, f(x), at a tourist destination is a function of time, in months. Using the graph of f(x), find f(4).
5
Select the transformations of h(x) = -3|x - 4| + 5 as it relates to the parent function. Select all that apply. (Note: Parent function - f(x) = |x|)
Select the transformations of h(x) = -3|x - 4| + 5 as it relates to the parent function. Select all that apply. (Note: Parent function - f(x) = |x|)
For f(x) = 3x + 2 and h(x) = x^2 -1, find the value of 4[f(-2) + h(3)]. (Hint: Recall that the number in parentheses is what you plug in for x.)
For f(x) = 3x + 2 and h(x) = x^2 -1, find the value of 4[f(-2) + h(3)]. (Hint: Recall that the number in parentheses is what you plug in for x.)
16
For f(x) = -2x + 3, find the value of f(3) - f(4).
For f(x) = -2x + 3, find the value of f(3) - f(4).
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Find the range of the function below if the domain is {-2, 1, 3}. (Note: Domain = x-values)
Find the range of the function below if the domain is {-2, 1, 3}. (Note: Domain = x-values)
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The distance, f(x), from a house to a cafe is a function of time. Using the graph of f(x), find f(7.5).
The distance, f(x), from a house to a cafe is a function of time. Using the graph of f(x), find f(7.5).
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Select the transformations of k(x) = 2|-x + 3| - 4 as it relates to the parent function. Select all that apply.
Select the transformations of k(x) = 2|-x + 3| - 4 as it relates to the parent function. Select all that apply.
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Write an equation for the nth term of the arithmetic sequence 10, 8, 6, 4, ... (Note: a_n = a_1 + (n - 1)d).
Write an equation for the nth term of the arithmetic sequence 10, 8, 6, 4, ... (Note: a_n = a_1 + (n - 1)d).
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What is the slope of the line that passes through (-3, 5) and (3, 6)?
What is the slope of the line that passes through (-3, 5) and (3, 6)?
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Which equation models the line on the graph? (Note: Use 2 points to find slope. Use where the line crosses the y-axis to find the y-intercept.)
Which equation models the line on the graph? (Note: Use 2 points to find slope. Use where the line crosses the y-axis to find the y-intercept.)
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Find the value of n so that the line through the points has the given slope. (4, 6) and (n, -2) and slope = 1/2
Find the value of n so that the line through the points has the given slope. (4, 6) and (n, -2) and slope = 1/2
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Which equation models the line on the graph? (Note: These are in point-slope form! Find the slope and use one point to create the equation.)
Which equation models the line on the graph? (Note: These are in point-slope form! Find the slope and use one point to create the equation.)
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Sopha owns a cafe on the verge of shutting down. She charges $7.50 for 3 pancakes and a cup of coffee. She charges $3.00 for one pancake and a cup of coffee. How much does Sopha charge for a pancake? How much does she charge for a cup of coffee?
Sopha owns a cafe on the verge of shutting down. She charges $7.50 for 3 pancakes and a cup of coffee. She charges $3.00 for one pancake and a cup of coffee. How much does Sopha charge for a pancake? How much does she charge for a cup of coffee?
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BrightTalk Mobile charges $0.25 per minute plus a monthly base fee. In August, Sarah used 150 minutes, and her bill was $45. Write and solve an equation to find the cost of the monthly base fee.
BrightTalk Mobile charges $0.25 per minute plus a monthly base fee. In August, Sarah used 150 minutes, and her bill was $45. Write and solve an equation to find the cost of the monthly base fee.
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Use your equation to find the cost if Sarah uses 180 minutes in September.
Use your equation to find the cost if Sarah uses 180 minutes in September.
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Which equation represents a line passing through the point (4, 2) with a slope of -2?
Which equation represents a line passing through the point (4, 2) with a slope of -2?
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Write the equation of the line that passes through (-6, -2) and is perpendicular to y = 3/2x - 5.
Write the equation of the line that passes through (-6, -2) and is perpendicular to y = 3/2x - 5.
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Which equation models the line graphed below in point-slope form? (Hint: y - y1 = m(x - x1))
Which equation models the line graphed below in point-slope form? (Hint: y - y1 = m(x - x1))
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Determine the values of A, B, and C when y - 3 = 4(x + 2) is written in standard form. Show your work.
Determine the values of A, B, and C when y - 3 = 4(x + 2) is written in standard form. Show your work.
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The scatter plot shows the average price of a National Football League ticket from 2007 to 2016.
a) Use the points (2007, 67.11) and (2016, 92.98) to write an equation of the line of fit in slope-intercept form. Let x be the number of years since 2006. Show your work.
b)
If the trend continues, what will be the price of a ticket in 2030?
The scatter plot shows the average price of a National Football League ticket from 2007 to 2016.
a) Use the points (2007, 67.11) and (2016, 92.98) to write an equation of the line of fit in slope-intercept form. Let x be the number of years since 2006. Show your work. b) If the trend continues, what will be the price of a ticket in 2030?
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Solve and graph -2y > 10.
Solve and graph -2y > 10.
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Which inequalities have no solution? Select all that apply.
Which inequalities have no solution? Select all that apply.
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Javier is taking part in a charity event at his school. Candy is being sold for $3 per bag and cookies are being sold for $6 per bag. What inequality represents the number of bags of candies (x) and the number of bags of cookies (y) that need to be sold to raise at least $600?
Javier is taking part in a charity event at his school. Candy is being sold for $3 per bag and cookies are being sold for $6 per bag. What inequality represents the number of bags of candies (x) and the number of bags of cookies (y) that need to be sold to raise at least $600?
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Solve -8y < -3y + 5 for y.
Solve -8y < -3y + 5 for y.
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Select the possible solutions of 15x ≥ 10 + 12x. Select ALL that apply.
Select the possible solutions of 15x ≥ 10 + 12x. Select ALL that apply.
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Which graph shows 5x ≥ 20 or -x - 14 < -16?
Which graph shows 5x ≥ 20 or -x - 14 < -16?
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Select the possible solutions of 8z - 4 ≤ 3z + 7. Select ALL that apply.
Select the possible solutions of 8z - 4 ≤ 3z + 7. Select ALL that apply.
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Which graph shows the solution for 1 < 3x - 2 < 10?
Which graph shows the solution for 1 < 3x - 2 < 10?
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Which graph shows 2(3x - 7) < -14 or 3x + 10 > 13?
Which graph shows 2(3x - 7) < -14 or 3x + 10 > 13?
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Solve and graph 8(-x + 1) ≥ -65 and 9 - 8x > -79 on a number line.
Solve and graph 8(-x + 1) ≥ -65 and 9 - 8x > -79 on a number line.
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A thermometer is accurate within 0.3 degrees Fahrenheit.
a) Write an absolute value inequality that represents the possible actual temperature t if the thermometer reads 68.5°F.
b) Solve the inequality and graph it on a number line.
A thermometer is accurate within 0.3 degrees Fahrenheit. a) Write an absolute value inequality that represents the possible actual temperature t if the thermometer reads 68.5°F. b) Solve the inequality and graph it on a number line.
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Solve the inequality |2y + 5| < 15. Then, graph your solution.
Solve the inequality |2y + 5| < 15. Then, graph your solution.
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Graph the inequality 3/2x + 5 - y < 6. Give one point that is a solution.
Graph the inequality 3/2x + 5 - y < 6. Give one point that is a solution.
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Match each of the 3 graphs to its inequality
i) 3x + 6y > -18
ii) 6x + 6y < -18
iii) 6x - 6y > -18
For which graph is (7, 0) a solution?
Match each of the 3 graphs to its inequality i) 3x + 6y > -18 ii) 6x + 6y < -18 iii) 6x - 6y > -18
For which graph is (7, 0) a solution?
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Solve and graph the inequality |4x - 7| >11.
Solve and graph the inequality |4x - 7| >11.
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Which of the following represents a line parallel to the x-axis?
Which of the following represents a line parallel to the x-axis?
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Select all the ways the system of equations could be solved.
8x - 9y = 13
16x + 3y = 22
Select all the ways the system of equations could be solved.
8x - 9y = 13 16x + 3y = 22
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Solve the system of equations using substitution.
c - d = 6
c = 4d - 8
Solve the system of equations using substitution.
c - d = 6 c = 4d - 8
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Solve the system of equations using elimination.
1/2 e - f = 7
1/2 e + 5/2 f = 9
Solve the system of equations using elimination.
1/2 e - f = 7 1/2 e + 5/2 f = 9
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What is the value of x if Lines 1 and 2 are parallel?
Line 1: (1, 3) and (4, 7)
Line 2: (x, 10) and (2, 6)
What is the value of x if Lines 1 and 2 are parallel?
Line 1: (1, 3) and (4, 7) Line 2: (x, 10) and (2, 6)
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Graph the system of inequalities.
y ≥ 3x + 2
y < -x - 2
Graph the system of inequalities. y ≥ 3x + 2 y < -x - 2
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Sketch the solution to the system of inequalities on the graph.
x + y < 2
4x + y < -1
Sketch the solution to the system of inequalities on the graph.
x + y < 2 4x + y < -1
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Sketch the solution to the system of inequalities on the graph.
x ≥ -2
2x - 3y > 3
Sketch the solution to the system of inequalities on the graph.
x ≥ -2 2x - 3y > 3
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What is the value of x if Lines 1 and 2 are perpendicular?
Line 1: (3, 5) and (6, 9)
Line 2: (x, 4) and (5, 2)
What is the value of x if Lines 1 and 2 are perpendicular?
Line 1: (3, 5) and (6, 9) Line 2: (x, 4) and (5, 2)
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Some really old and really homemade cars are having a race. Car A is 10 feet behind the starting line and moves at a rate of 6 feet per second. Car B has cheated and is 25 feet ahead of the starting line. Car B also moves at a rate of 4 feet per second. The two racers of the cars want to know how many seconds, t, will pass before the two cars are at the same distance.
a) Write a system of equations that can be used to represent the situation.
b) Solve the system to figure out how many seconds will pass before the cars are the same distance from the starting line.
Some really old and really homemade cars are having a race. Car A is 10 feet behind the starting line and moves at a rate of 6 feet per second. Car B has cheated and is 25 feet ahead of the starting line. Car B also moves at a rate of 4 feet per second. The two racers of the cars want to know how many seconds, t, will pass before the two cars are at the same distance. a) Write a system of equations that can be used to represent the situation. b) Solve the system to figure out how many seconds will pass before the cars are the same distance from the starting line.
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Study Notes
Algebra B Midterm Study Guide
-
Module 3: Relations and Functions
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Problem 1: Given a graph of a function representing the number of people at a tourist destination as a function of time (in months). Find f(4).
- f(4) = 5 (The number of people at the destination when the time is 4 months.)
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Problem 2: Identify transformations from the parent function for h(x) = -3|x - 4| + 5.
- Reflection over x-axis
- Vertical stretch by a factor of 3
- Translated right 4 units
- Translated up 5 units
- Parent Function f(x) = |x|
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Problem 3: Evaluate 4[f(-2) + h(3)] for f(x) = 3x + 2 and h(x) = x² - 1.
- f(-2) = -4
- h(3) = 8
- 4[-4 + 8] = 16
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Problem 4: Find the value of f(3) - f(4) for f(x) = -2x + 3.
- f(3) = -3
- f(4) = -5
- -3 - (-5) = 2
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Problem 1: Given a graph of a function representing the number of people at a tourist destination as a function of time (in months). Find f(4).
Module 3: Relations and Functions (Continued)
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Problem 5: For the given function, find the range if the domain is {-2, 1, 3}.
- f(x) = x³ + x - 5/
- f(-2) = -15
- f(1) = -3
- f(3) = 25
- Range: {-15, -3, 25}
- f(x) = x³ + x - 5/
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Problem 6: Find the value of f(7.5) from a graph of the distance from a house to a cafe as a function of time.
- f(7.5) = 7.5
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Problem 7: Identify transformations of k(x) = 2|-x + 3| - 4 from the parent function.
- Reflection over the y-axis
- Horizontal translation left 3 units
- Vertical stretch by a factor of 2
- Vertical translation down 4 units -Parent Function:f(x)=|x|
Module 4: Linear and Nonlinear Functions
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Problem 8: Find the nth term of the arithmetic sequence 10, 8, 6, 4.
- a₄ = a₁ + (n-1)d
- an = -2n + 12
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Problem 9: Find the slope of a line passing through (-3, 5) and (3, 6).
- m = (6 - 5) / (3 - (-3)) = 1/6
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Problem 10: Find the slope of a line passing through (-3, 2) and (7, 2).
- m = (2-2)/(7 - (-3)) = 0
Module 4: Linear and Nonlinear Functions (Continued)
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Problem 11: Find the equation of the line in the given graph.
- The line passes through (0, 3) and (2, 4).
- m = 1/2
- b = 3
- y = 1/2 x + 3
Module 5: Creating Linear Equations
- Problem 16: BrightTalk Mobile charges $0.25 per minute plus a monthly base fee. Sarah’s bill for 150 minutes was $45.
- a) Find the monthly base fee. - Monthly base fee: $7.50
- b) Find the bill if she uses 180 minutes in September
- $52.50
- Problem 17: Find the equation of a line passing through (4, 2) with slope of 1/2. -y = (1/2)x + (1/2)or y = (1/2)x - 1)
Module 6: Linear Inequalities
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Problem 24: Solve $-2y > 10$
- y < -5
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Problem 25: Find inequalities with no solution
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Problem 26: Find inequality for number of bags of candy (x) and cookies (y) sold to raise $600 or more. -3x + 6y ≥ 600
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Problem 27: Solve -8y ≤ -3y + 5 for y
- y ≥ -1
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Problem 28: Select potential solutions to 15x ≥ 10 + 12x
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Problem 29: Identify graph solution to 5x ≥ or or -x-14 <-16
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Problem 30: Select correct potential solutions to 8(-4) ≤ 3z + 7
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Problem 31: Find graph of solution to 1 ≤ 3x − 2 < 10
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Problem 32: Find graph of solution 2(3x - 7) < -14 or 3x + 10 > 13
Module 7: Systems of Equations and Inequalities
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Problem 39: Find a horizontal line among given equations
- y = 9
- Problem 40: Select correct ways to solve system of equations
- Problem 41: Solve system of equations through substitution
- Problem 42: Solve system of equations through elimination
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Description
Prepare for your Algebra B midterm with this comprehensive study guide focusing on Module 3: Relations and Functions. Explore key concepts including function evaluation, transformations, and analysis of graphical data. Test your understanding with a variety of problems and sharpen your algebra skills for exam success.
