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Questions and Answers
Using the graph of f(x), find f(4)?
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 f(x) = |x|. Select all that apply.
Select the transformations of h(x) = -3|x - 4| + 5 as it relates to the parent function f(x) = |x|. Select all that apply.
For f(x) = 3x + 2 and h(x) = x² - 1, find the value of 4[f(-2) + h(3)]
For f(x) = 3x + 2 and h(x) = x² - 1, find the value of 4[f(-2) + h(3)]
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}.
Find the range of the function below if the domain is {-2, 1, 3}.
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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, ...?
Write an equation for the nth term of the arithmetic sequence 10, 8, 6, 4, ...?
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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 (4, 6) and (n, -2) has a slope of 1/2.
Find the value of n so that the line through the points (4, 6) and (n, -2) has a slope of 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 Sophia 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 Sophia 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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Using the equation you found, determine the cost of Sarah's bill in September if she uses 180 minutes.
Using the equation you found, determine the cost of Sarah's bill in September if she uses 180 minutes.
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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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Determine the values of A, B, and C when y - 5 = -2(x -1) is written in standard form. Show your work.
Determine the values of A, B, and C when y - 5 = -2(x -1) is written in standard form. Show your work.
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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.
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.
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If the trend from the scatter plot continues, what will the price of a ticket be in 2030?
If the trend from the scatter plot continues, what will the price of a ticket be in 2030?
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Solve and graph the inequality -2y > 10.
Solve and graph the inequality -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. Write an absolute value inequality that represents the possible actual temperature t if the thermometer reads 68.5°F. Solve the inequality and graph it on a number line.
A thermometer is accurate within 0.3 degrees Fahrenheit. Write an absolute value inequality that represents the possible actual temperature t if the thermometer reads 68.5°F. 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 x/3 + 5 - y < 6. Give one point that is a solution.
Graph the inequality x/3 + 5 - y < 6. Give one point that is a solution.
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Match each of the 3 graphs to its inequality (Note: See video on Google Classroom). For which graph is (7, 0) a solution?
Match each of the 3 graphs to its inequality (Note: See video on Google Classroom). 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
2c - 4d = 8
Solve the system of equations using substitution. c - d = 6 2c - 4d = 8
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Solve the system of equations using elimination. -1/2e + 4f = 7
f - e = 7
Solve the system of equations using elimination. -1/2e + 4f = 7 f - e = 7
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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. Write a system of equations that can be used to represent the situation.
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. Write a system of equations that can be used to represent the situation.
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Solve the system to figure out how many seconds will pass before the cars are the same distance from the starting line.
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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Given the function $g(x) = -2x^2 + 5$, what is the value of $g(-3) + g(2)$?
Given the function $g(x) = -2x^2 + 5$, what is the value of $g(-3) + g(2)$?
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The points (2, a) and (5, 1) are on a line with a slope of -2. What is the value of a?
The points (2, a) and (5, 1) are on a line with a slope of -2. What is the value of a?
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Write the equation of the line in slope-intercept form that passes through the point (2, -5) and has the same slope as the line $y= rac{3}{4}x + 2$?
Write the equation of the line in slope-intercept form that passes through the point (2, -5) and has the same slope as the line $y= rac{3}{4}x + 2$?
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What are all the integer values of x such that $2x - 8 < 3$ and $5x + 1 \ge -14$?
What are all the integer values of x such that $2x - 8 < 3$ and $5x + 1 \ge -14$?
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Solve the following system of equations: $y = -2x + 7$ and $3x - 2y = -3$.
Solve the following system of equations: $y = -2x + 7$ and $3x - 2y = -3$.
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Study Notes
Algebra B Midterm Study Guide
-
Module 3: Relations and Functions
- Problem 1: Given a graph showing the number of people at a tourist destination over time (in months), find f(4). Answer: f(4) = 5.
- Problem 2: Select transformations of h(x) = -3|x - 4| + 5 relative to the parent function f(x) = |x|. Answers: Vertical stretch by a factor of 3, Translated right 4 units, Translated up 5 units.
- Problem 3: Given f(x) = 3x + 2 and h(x) = x² - 1, find 4[f(-2) + h(3)]. Answer: 16.
- Problem 4: Given f(x) = -2x + 3, find f(3) - f(4). Answer: 2.
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Problem 5: Find the range of the function f(x) = x³ + x - 5/3 for the domain {-2, 1, 3}. Answers: {-15, -3, 25}.
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Problem 6: Find f(7.5) from a graph depicting distance from a café over time (in minutes). Answer: f(7.5) = 7.5.
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Problem 7: Select transformations of k(x) = 2|-x + 3| - 4 relative to the parent function f(x) = |x|. Answers: Reflected over the y-axis, Translated left 3 units, Vertical stretch by a factor of 2, Translated down 4 units.
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Module 4: Linear and Nonlinear Functions
- Problem 8: Find the nth term of the arithmetic sequence 10, 8, 6, 4. Answer: an = -2n + 12.
- Problem 9: Find the slope of the line passing through (-3, 5) and (3, 6). Answer: 1/6.
- Problem 10: Find the slope of the line passing through (-3, 2) and (7, 2). Answer: 0.
- Problem 11: Find the equation of the line graphed, given points on the line. Answer: y = (1/2)x + 3.
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Module 5: Creating Linear Equations
- Problem 16: BrightTalk Mobile charges $0.25 per minute plus a monthly base fee. If Sarah's August bill was $45 for 150 minutes, find the monthly base fee. Answer: $7.50. Find the cost if she uses 180 minutes in September, answer: $52.50.
- Problem 17: Find the equation of a line with a slope of 1/2 and passing through (4, 2). Answer: y = (1/2)x - 1.
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Module 6: Linear Inequalities
- Problem 24: Solve and graph -2y > 10. Answer: y < -5.
- Problem 25: Identify inequalities with no solution. (List needed)
- Problem 26: Javier is selling candy and cookies. Find the inequality representing the number of candy bags (x) and cookie bags (y) needed to raise at least $600. Answer: 3x + 6y ≥ 600.
- Problem 27: Solve -8y < -3y + 5 for y. Answer: y > -1.
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Module 7: Systems of Equations and Inequalities and much more... (List needed)
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Prepare for your Algebra B midterm with this comprehensive study guide. Covering topics such as relations, functions, and transformations, each problem will challenge your understanding and application of key concepts. Perfect for students looking to reinforce their skills in algebra.
