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Questions and Answers
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) = x² - 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) = x² - 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)
f(x) = x³ + x - 5
Find the range of the function below if the domain is {-2, 1, 3}. (Note: Domain = x-values)
f(x) = x³ + x - 5
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The distance, f(x), from a house to a café is a function of time. Using the graph of f(x), find f(7.5).
The distance, f(x), from a house to a café 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)? (Note: m = (y_2 - y_1) / (x_2 - x_1) )
What is the slope of the line that passes through (-3, 5) and (3, 6)? (Note: m = (y_2 - y_1) / (x_2 - x_1) )
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What is the slope of the line that passes through (-3, 2) and (7, 2)?
What is the slope of the line that passes through (-3, 2) and (7, 2)?
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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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Sophia 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?
Sophia 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.
a) 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. a) Write and solve an equation to find the cost of the monthly base fee.
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B) Use your equation to find the cost if Sarah uses 180 minutes in September.
B) 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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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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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.
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.
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B) If the trend continues, what will be the price of a ticket in 2030?
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.
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.
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B) Solve the inequality and graph it on a number line.
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 3/2 x + 5 - y < 6. Give one point that is a solution.
Graph the inequality 3/2 x + 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
Match each of the 3 graphs to its inequality. i) 3x + 6y > -18 ii) 6x + 6y < -18 iii) 6x - 6y > -18
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For which graph is (7, 0) a solution?
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
-e + 4f = 7
2
-e - f = 9
Solve the system of equations using elimination. 1 -e + 4f = 7
2 -e - 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.
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.
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B) Solve the system to figure out how many seconds will pass before the cars are the same distance from the starting line.
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
- Problem 1: Given a graph of the number of people at a tourist destination as a function of time (in months), find the value of f(4).
- Answer: f(4) = 5
- Problem 2: Identify transformations of the function h(x) = -3|x - 4| + 5 relative to the parent function f(x) = |x|.
- Possible Transformations: Reflection over the x-axis, Vertical stretch by a factor of 3, Horizontal shift right 4 units, and Vertical shift up 5 units.
- Problem 3: Evaluate 4[f(-2) + h(3)] given f(x) = 3x + 2 and h(x) = x² - 1.
- Answer: 16
- Problem 4: Find the value of f(3) - f(4) for f(x) = -2x + 3.
- Answer: 2
-
Problem 5: Determine the range of a function given a domain of {-2, 1, 3}.
- Function: f(x) = x³ + x - (5/3)
- Range: {-15, -3, 25}
-
Problem 6: Find the value of f(7.5) from a graph showing distance from a café as a function of time (in minutes).
- Answer: f(7.5) = 7.5
-
Problem 7: Identify transformations of k(x) = 2|-x + 3| - 4 relative to the parent function f(x) = |x|.
- Possible Transformations: Reflection about the y-axis, Vertical stretch by a factor of 2, Horizontal shift left 3 units, Vertical shift down 4 units
-
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: Calculate the slope of a line passing through (-3, 5) and (3, 6).
- Answer: 1/6
- Problem 10: Find the slope of a line passing through (-3, 2) and (7, 2).
- Answer: Undefined
- Problem 11: Determine the equation of a linear line on a graph.
- Points: (2, 4) (0, 3) (-6,0)
- Equation: y = (1/2)x + 3
-
Module 5: Creating Linear Equations
- Problem 16a: Find the monthly base fee for a mobile service plan.
- Info: $45 bill for 150 minutes used in August
- Rate: $0.25 per minute
- Answer: $7.50
- Problem 16b: Find the cost if Sarah uses 180 minutes in September.
- Answer: $52.50
- Problem 17: Find the equation of a line with slope (1/2) that passes through (4, 2).
- Answer: y = (1/2)x - 1
-
Module 6: Linear Inequalities
- Problem 24: Solve and graph -2y >10.
- Answer: y < -5
- Problem 25: Identify inequalities with no solutions.
- Solutions: 3x + 5 < 3x + 7, 2(x – 4) ≤ 2(2x + 3) and 5x + 8 ≥ - 5(x + 2)
- Problem 26: Write an inequality to represent the number of bags of candy (x) and cookies (y) sold to raise at least $600.
- Answer: 3x + 6y ≥ 600
- Problem 27: Find y given –8y < -3y + 5.
- Answer: y > -1
-
Module 7: Systems of Equations and Inequalities
- Problem 39: Identify a horizontal line.
- Answer: y = a constant
- Problem 40: Choose valid methods for solving a system of equations.
- Valid Methods: Multiplying either equation by a constant and then adding or subtracting.
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Description
This study guide focuses on Module 3 covering relations and functions in Algebra B. It features problem-solving techniques involving function evaluation, transformations, and range determination. Perfect for students preparing for the midterm exam.
