Function Notation & Composition
If f(x)=3x-7), find f(4).
5
Do the points (1, 4), (2, 4), and (3, 7) represent a function?
Yes. Each input has exactly one output.
An even function’s graph is symmetric across which axis?
The y-axis.
The point (3, −8) lies on a function’s graph. What point lies on its inverse relation?
(−8, 3)
Which planet is known as the Red Planet?
Mars
If f(x) = x² − 2x, find f(−3).
15
What is the y-intercept of f(x) = x² − 6x + 8?
(0, 8)
If f is odd and f(6) = −9, what is f(−6)?
9
What graphical test determines whether a function is one-to-one?
The horizontal line test.
What is the largest ocean on Earth?
The Pacific Ocean
If f(x) = 5 − 2x, solve f(x) = 17.
x = −6
State the domain of g(x) = (x + 2)/(x − 5).
All real numbers except 5.
A room’s temperature increases from 62°F at t = 2 hours to 77°F at t = 5 hours. Find the average rate of change.
5°F per hour.
A one-to-one function contains the points
(−2, 7), (0, 3), and (5, −4).
Find f⁻¹(7) + f⁻¹(−4).
3
How many hearts does an octopus have?
Three
If f(x) = x² + 1 and g(x) = 3x − 2,
find f(g(−1)).
26
For f(x) = (x − 3)² − 4, state the minimum value and where the function is decreasing.
Minimum: −4. Decreasing when x < 3.
Find the average rate of change of
f(x) = x² − 3x from x = −2 to x = 4.
−1
A one-to-one function has domain −4 ≤ x ≤ 6 and range 2 ≤ y ≤ 11. State the domain and range of its inverse.
Domain: 2 ≤ x ≤ 11. Range: −4 ≤ y ≤ 6.
What is the only mammal capable of sustained, powered flight?
A bat
If f(x) = 2x − 3 and g(x) = x² + 4,
solve f(g(x)) = 23.
x = 3 or x = −3
For g(x) = 9 − (x + 1)², find both zeros and where g(x) > 0.
Zeros: −4 and 2. Positive when −4 < x < 2.
An odd function has f(2) = 7 and f(6) = −5. Find its average rate of change from x = −6 to x = 2.
1/4
For f(x) = (x − 2)², give two different domain restrictions that each make its inverse a function. Explain why they work.
x ≥ 2 or x ≤ 2. Either restriction makes the function one-to-one.
Which planet takes longer to rotate once on its axis than to complete one orbit around the Sun?
Venus