Functions & Notation
Domain & Range
Tranformation
Linear Function
Average Rate of Change
100
What is a function?
A relation where every input has exactly one output.
100
Find the domain of the function: f(x)=x2−4
(−∞,∞)
100
Describe the transformation from f(x)=x2 to g(x)=x2+4
Shift up 4 units
100
Find the slope of the line passing through (2,5) and (6,13)
2
100
Find the average rate of change of f(x)=x2 from x=1 to x=3
4
200
If f(x) = 3x - 2, find f(5)
13
200
State the range of the function: f(x)=∣x−2∣+1
[1,∞)
200
Describe the transformation from f(x)=x2 to g(x)=(x−5)2
Shift right 5 units
200
Write an equation with slope 2 and y-intercept 5
y = 2x+5
200
Find the average rate of change of f(x)=5x−2 from x=0 to x=4
5
300
What is composition?
This notation represents plugging one function into another.
300
Determine the domain of the function: f(x)=2/(x−5)
(−∞,5)∪(5,∞)
300
Describe the transformation from f(x)=x2 to g(x)=−(x2)
Reflection over the x-axis
300
Is f(x)=−4x+7 increasing or decreasing?
decreasing
300
Find the average rate of change of f(x)=x+6 from x=2 to x=8
1
400
Based on the table, what is f(g(3))?
5
400
The graph of a function has a maximum value of 7 and extends forever left and right. What is the range of the function?
(−∞,7]
400
Describe the transformations from f(x)=x2 to g(x)=2(x+1)2−3
1. Shift left 1
2. Vertical stretch by factor of 2
3. Shift down 3
400
Find f(4) if f(x)=2x+1
9
400
y=2x+5
Find the average rate of change of f(x)=x2 from x=2 to x=5
7
500
A phone plan charges a $20 base fee plus $5 per GB of data used. This function represents the total cost C(d).
C(d) = 5d + 20
500
A school is selling tickets for a fundraiser. The profit made is modeled by the function:
P(x)=500/(x−25)
where x is the number of tickets sold. What is the domain of the function?
(−∞,25)∪(25,∞)
500
A ball’s height is modeled by
h(t)=−(t−2)2+5
where t is time in seconds.
Describe the transformations from f(t)=t2
1. Shift right 2
2. Shift up 5
3. Reflect over the x-axis
500
A streaming service charges $10 per month plus a $15 sign-up fee. Write a function for the total cost after m months.
C(m) = 10m+15
500
A babysitter earns $14 per hour. Find the average rate of change in earnings from 3 hours to 7 hours.
$14 per hour