Function Notation
f(x)=2x+3 , what is f(4) ?
11
A gym charges $20 per month for up to 10 visits and $2 for each additional visit. Find the cost of 12 visits.
$24
A movie theater only sells tickets to people between 3 and 65 years old, inclusive. What is the domain of possible ages for ticket buyers?
3 ≤ x ≤ 65
If f(x) = 2x, what is the average rate of change from x=2 to x=5 ?
2
Find the inverse function of:
f(x) = 3x + 5
f(x) = (x - 5) / 3
Given g(x)=x2−5 , find g(−2) .
-1
Use the piecewise function to find C(3)
C(m) = 4m if m ≤ 1 and 2m if m > 1
6
A cell phone plan charges $20 per month for up to 5 GB of data. What is the domain for the amount of data (in GB) that can be used without extra charges?
0 ≤ x ≤ 5
If f(x) = x², what is the average rate of change from x=1 to x=4 ?
5
Find the inverse function of:
f(x) = x/2 + 7
f(x) = 2(x - 7)
If h(x)=3x−7 , what value of x makes h(x)=5 ?
4
A mobile plan charges $10 for up to 100 texts and $0.10 for each text beyond that. Write a piecewise function that models the total cost C for t texts.
C(t) = 10 if x ≤ 100 and C(t) = 10 + 0.1t if x > 100
A function models the height (in meters) of a plant over time (in weeks), and the plant cannot have negative height. What is the domain for the height of the plant?
x≥0
If f(x) = x² - 2x, what is the average rate of change from x=0 to x=3 ?
1
Find the inverse function of:
f(x) = 2x²
f(x) = √(x/2)
Given k(x)= 2x - x, find k(a + 1) in terms of a.
a + 3
A parking lot charges $5 for up to 2 hours and $3 for every hour after that. Write a piecewise function that gives the total cost given the number of hours, h.
C = 5 if h ≤ 2 and c = 5 + 3x if h >2
A function g(x) gives the number of tickets left for an event, starting at 100 and decreasing to 0 as tickets are sold. What is the range of g(x)?
0 ≤ x ≤ 26
If h(x) increases from 10 to 26 as x goes from 2 to 6, what is the average rate of change?
4
Find the inverse function of:
f(x) = 4 - x
f(x) = -(x - 4)
If m(x) = 3x - 5 and m(t) = 4, find the value of t.
3
A streaming service charges $8 for the first month and $6 for each additional month. Find the total cost for 7 months.
$44
A function models the number of hours a machine can run before it needs maintenance, which is between 50 and 200 hours. What is the domain for the number of hours?
50 ≤ x ≤ 200
If h(x) increases from 2 to 24 as x goes from 2 to 13, what is the average rate of change?
2
Find the inverse function of:
f(x) = √(x - 4)
f(x) = x² + 4