Transformations
The graph of the function f(x) = x² is shifted 4 units to the right and 2 units up to create a new function g(x). Write the equation for g(x) and describe the transformations applied to f(x).
g(x) = (x - 4)^2 + 2
What is the equation in slope-intercept form of the line that passes through the point (2, −2) and is perpendicular to the line represented by y = 2/5x + 2?
y=-5/2x+3
What is the solution to 34x + 95 = 3(14x + 9)?
17/2
Which expression is equivalent to √96?
4√6
Jessica weighs 87 pounds and wants to gain weight. After 5 weeks, she weighs 97 pounds. What is her average rate of change?
2
The function f(x) = |x| is reflected over the x-axis and then shifted down 3 units to create a new function g(x). Write the equation for g(x) and describe the transformations applied to f(x).
g(x) =-lxl-3
Sarah is saving money to buy a new bicycle. She already has $50, and she saves $15 each week from her allowance. Write an equation that represents the total amount of money (A) Sarah will have after w weeks.
A = 15w + 50
What is the solution to −(6m + 8) = 4(17 − m)?
m=-38
Which expression is equivalent to −28x2 + 35x?
−7x x (4 − 5)
A plant grows 2 inches per week. How much will it grow in 5 weeks?
10 inches
The graph of the function f(x) = x is vertically stretched by a factor of 2 and then shifted 5 units to the left to create a new function g(x). Write the equation for g(x) and describe the transformations applied to f(x).
g(x) = 2(x + 5)
A movie theater charges a $6 admission fee plus $3 for each snack purchased. Write an equation that represents the total cost (C) for a person who buys s snacks at the theater.
C=3s+6
What are the solutions to (x + 7)2 = 81?
-16 and 2
Which expression is equivalent to x2 − 17x − 60?
(x − 20)(x + 3)
You earn $12 per hour. How much will you earn if you work for 25 hours?
$300
A rectangle has a length of 4 units and a width of 2 units. The rectangle is translated 3 units to the right and 5 units up on the coordinate plane. Write the coordinates of the rectangle’s vertices after the transformation and describe the transformation that was applied.
(3, 5), (7, 5), (7, 7), and (3, 7)
Jason has twice as many marbles as Emily. Together, they have 18 marbles. How many marbles does each person have? Write an equation to represent the situation and solve it.
( 2 x 6 = 12 ) marbles.
What is the solution set for −4x + 10 ≥ 5x + 55?
x ≤ -5
A rectangle has a length of ( 3x + 4 ) centimeters and a width of ( 2x - 1 ) centimeters. Write and simplify an expression for the perimeter of the rectangle.
( 10x + 6 ) centimeters
A water tank is being filled at a constant rate. After 2 hours, the tank contains 60 liters of water. After 5 hours, the tank contains 150 liters of water. What is the rate at which water is being added to the tank?
30 liters per hour
The graph of the function f(x) = x² is reflected over the y-axis and then shifted 7 units down to form a new function g(x). Write the equation for g(x) and describe each transformation applied to f(x).
g(x) = x^2 - 7)
Sarah bought 5 notebooks and a pen. Each notebook costs $3, and the pen costs $x. If she spent a total of $19, what is the cost of the pen? Write and solve an equation.
( 5 x 3 + x = 19 )
What is the solution to 4(q + 56.5) = 30q − 112?
q=13
Maria is buying pencils and erasers. Each pencil costs $2 and each eraser costs $1. If she buys ( p ) pencils and ( e ) erasers, write an expression for the total cost and simplify it.
( 2p + e )
A plant was 12 cm tall on Monday. By Thursday, it had grown to 24 cm. What was the average rate of change in the plant’s height, in centimeters per day, during this period?
4 cm per day