Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each element in the domain is paired with exactly one element in the range.

Question 2

Given the set of ordered pairs $$\{(2, 5), (3, 7), (2, 8)\}$$, does this set represent a function?

Accepted Answer

No, because the input 2 is paired with two different outputs.

Question 3

If $$f(x) = 3x + 7$$, what is $$f(-2)$$?

Accepted Answer

$$f(-2) = 1$$

Question 4

Which of the following equations does NOT define $$y as a $$function of $$x$$?

Accepted Answer

$$x = y^2$

Question 5

Find the domain of the function $$f(x) = \frac{1}{x-4}.$$

Accepted Answer

$$(-\infty, 4) \cup (4, \infty)$$

Question 6

Given $$f(x) = x^2$ and g(x) = x + 1$, what is (f + g)(2$$)$$?

Accepted Answer

$$(f + g)(2) = 7$$

Question 7

If $$f(x) = x^2$ - 3x$$ and $$h = 2$$, what is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x - 3 + h$$

Question 8

A cube has side length $$s. $$Express the volume $$V as a $$function of $$s$$ and state the domain.

Accepted Answer

$$V(s) = s^3$, domain: $$[0, \infty)$$

Question 9

Given $$f(x) = \sqrt{x-1}$$, what is the domain of $$f$$?

Accepted Answer

$$[1, \infty)$$

Question 10

If $$f(x) = x^2$ and g(x$$) = \frac{1}{x}$$, what is the domain of (f$$ \cdot g)(x)$$?

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 11

Which of the following real-world scenarios is best modeled by a function?

Accepted Answer

Assigning each person in a city to their unique social security number.

Question 12

Given $$f(x) = x^2$ and g(x) = x - 3$, find (f - g)(4$$)$$.

Accepted Answer

$$(f - g)(4) = 16 - 1 = 15$$

Question 13

If $$f(x) = \sqrt{x-2}$$ and $$g(x) = \frac{1}{x-5}$$, what is the domain of $$(f + g)(x)$$?

Accepted Answer

$$[2, 5) \cup (5, \infty)$$

Question 14

Evaluate the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for $$f(x) = 2x + 1.$$

Accepted Answer

$$2$$

Question 15

Which of the following is NOT a valid function notation?

Accepted Answer

$$f(x, y)$$ for a function of one variable$

Question 16

If $$f(x) = x^2$ and g(x) = x + 2$, what is $$\left(\frac{f}{g}\right)(3)$$?

Accepted Answer

$$\frac{9}{5}$$

Question 17

Which of the following best describes the range of a function?

Accepted Answer

The set of all possible output values.

Question 18

Given $$f(x) = \sqrt{9 - x^2$}$$, what is the domain of $$f$$?

Accepted Answer

$$[-3, 3]$$

Question 19

If $$f(x) = x^2$ and g(x) = 2x$, what is (f$$ \cdot g)(-1)$$?

Accepted Answer

$$(f \cdot g)(-1) = 2$$

Functions and Their Graphs: Precalculus Study Notes

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