Functions Quiz
Questions: 16 · 10 minutes
1. Let f(x) = x + 2 and g(x) = 3x. What is (f ∘ g)(2)?
6
12
10
8
2. Which statement best defines a mathematical function?
A relation that may assign several outputs to a single input
A relation in which every output must come from only one input
A relation that assigns exactly one output to each input
Any equation containing both an input variable and an output variable
3. The function f(x) = x² has all real numbers as its domain. Why does its inverse relation fail to be a function?
Squaring is not defined for negative inputs
The graph of f fails the vertical line test
The range of f includes every real number
Distinct inputs such as -2 and 2 produce the same output
4. A graph represents y as a function of x when which condition is met?
Every vertical line crosses the graph at most once
The graph crosses the x-axis no more than once
The graph crosses the y-axis exactly once
Every horizontal line crosses the graph exactly once
5. A piecewise function is defined by h(x) = x + 4 when x < 0 and h(x) = x² when x ≥ 0. What is h(-3) + h(2)?
5
4
1
9
6. At which x-value does r(x) = 1/(x + 4) have a vertical asymptote?
At x = 0, because the numerator is constant
At x = 4, because 4 appears in the denominator
There is no vertical asymptote because the function is rational
At x = -4, because that input makes the denominator zero
7. What is the average rate of change of f(x) = x² from x = 1 to x = 3?
4
2
8
10
8. If f(x) = 2x - 3, what is f(5)?
7
2
10
13
9. Compared with y = x², how is the graph of y = (x - 2)² + 3 translated?
2 units left and 3 units up
3 units right and 2 units up
2 units right and 3 units up
2 units right and 3 units down
10. A table contains the points (0, 5), (1, 8), (2, 11), and (3, 14). Which rule matches the table?
f(x) = x + 5
f(x) = 5x + 3
f(x) = 3x + 2
f(x) = 3x + 5
11. For f(x) = √(x - 4), which inputs are permitted when working with real numbers?
Only real numbers strictly below 4
The number 4 and every real number greater than it
The number 4 and every real number less than it
Every real number other than 4
12. Which inputs are zeros of f(x) = x² - 9?
Only x = 9
x = -3 and x = 3
x = -9 and x = 9
Only x = 3
13. Which formula represents an exponential function?
y = x² + 3
y = 2x + 3
y = 3 · 2ˣ
y = 3/x
14. If f(x) = 2x + 5, which formula gives f⁻¹(x)?
Double the input and subtract 5: 2x - 5
Subtract 5 from the input, then divide by 2: (x - 5)/2
Add 5 to the input, then divide by 2: (x + 5)/2
Take the reciprocal of the original expression: 1/(2x + 5)
15. Which set of ordered pairs represents a function?
{(1, 2), (1, 3), (2, 4)}
{(-1, 0), (-1, 2), (0, 3)}
{(1, 2), (2, 3), (3, 2)}
{(0, 1), (2, 3), (2, 4)}
16. A taxi ride costs a fixed $4 fee plus $2.50 per mile. If m is the number of miles traveled, which function gives the total cost C(m)?
C(m) = 4m + 2.50
C(m) = 4 + 2.50m
C(m) = 6.50m
C(m) = 2.50(m + 4)