Properties of Functions
Piecewise Functions
Rate of Change
Transformations
Word Problems
100
The value of f(x) at x=3
f(x)=2
100
f(5) for the following function:
f(x) = {(2x,+,5 if x>2),(2x,-,5 if x<=2):}
f(5) = 15
100
Using this table, give the average rate of change (in dollars) from 2023 to 2026.
$10 per year
100
Describe the transformation that occurs when y=f(x) becomes y=2f(x)+3 .
Vertical stretch by a factor of 2, shift upwards 3 units
100
Solve for x.
|-3+2x|=11
x={-4,7}
200
The domain and range of the function f(x) = 2sin(x) +1 
D:(-oo,oo)
R:[-1,3]
200
The piecewise function that represents the following graph
f(x) = {(2x,-,4,ifx<2),(-x,+,5,ifx>=2):}
200
Find the average rate of change from x = -3 to x = 5.
3/8
200
List the transformations in order when y=x^2 becomes y=(3x+2)^2-6
1. Horizontal stretch by a factor of 3
2. Shift left by 2 units
3. Shift down by 6 units
200
Solve for s.
2^(5s+3)=8^(3s-3)
s=3
300
The equation (in slope-intercept form) of the line that goes through the point (-6, 4) and has a slope of -2
y = -2x - 8
300
Graph the following piecewise function:
f(x)={(2,if0<=x<1),(3,if1<=x<2),(4,if2<=x<3):}
300
The linear function that represents the following description:
In 2005, Bryan was 140 cm tall. He has grown approximately 3.5 cm per year since then.
f(x)=140+3.5x
where f(x) is Bryan's height in year x
300
The transformed function f'(x)=-4(x-3)^3+2 . Identify the parent function and list its transformations.
Parent function: f(x) = x^3
1. Shift right by 3 units
2. Vertical stretch by a factor of 4
3. Reflect across the x-axis
4. Shift up 2 units
300
Solve for p by factoring the expression completely.
p^3-2p^2-24p=0
p={-4,0,6}
400
The equation of the line that passes through the point (2, -4) and is perpendicular to the line y=5x
y+4=-1/5(x-2)
400
Graph the following piecewise function:
f(x) = {(3,if x<=-4),(x+2, if -4<x<=2),(-x+4, if x>2):}
400
Find the average rate of change of the function f(x) = x^2-8x+5 on the interval [-1,3]
(f(b)-f(a))/(b-a)=(-10-(14))/(3-(-1))=-6
400
Transform the following points using 2f(x+1)^2-3
(0,1) (1,2) (2,0)
(-1,-1)(0,1)(1,-3)
400
Simplify the expression.
(x^-3y^5z^-1)/(x^-2y^2z)
y^3/(xz^2)
500
The domain and range of the function 1/(x-2)
D: (-oo,2)U(2,oo)
R: (-oo,0)U(0,oo)
500
The equation of the following function:
f(x) = {(-2,ifx> -2),(-1/2x-1,if-2<x<=2),(x,if x>2):}
500
The average rate of change in monthly rainfall (in mm) from June to September.
-4.41 mm per month
500
The equation of f'(x) if f(x) = sqrtx is shifted up 3 units, shifted left 2 units, shrinks vertically by a factor of 4, and is reflected across the x-axis.
f'(x) = -1/4sqrt(x+2)+3
500
Given f(x)=3x+2 , find
(f(x+h)-f(x))/h
3