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 $$\{(2, 5), (3, 7), (2, 8), (4, 9)\}$$, does this set represent a function?

Accepted Answer

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

Question 3

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(-2)$$?

Accepted Answer

$$15$$

Question 4

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

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 5

The domain of the function $$f(x) = \dfrac{1}{x-4} is$$:

Accepted Answer

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

Question 6

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

Accepted Answer

$$(-\infty, 2.5]$$

Question 7

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

Accepted Answer

$$x^2 + x + 1$

Question 8

A cube has side length $$s. $$Express the volume $$V as a $$function of $$s$$ and state the domain in the context of real-world applications.

Accepted Answer

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

Question 9

If $$f(x) = x^2$ + 1$$ and $$g(x) = x - 2$$, find $$(f \cdot g)(x).$$

Accepted Answer

$$(x^2 + 1)(x - 2$$)$$

Question 10

Find the difference quotient for $$f(x) = x^2$.

Accepted Answer

$$\dfrac{(x+h)^2$ - x^2$}{h}$$

Question 11

Given the relation shown by the mapping: $$\{(1, 2), (2, 3), (3, 4), (1, 5)\}$$, is this a function?

Accepted Answer

No, because the input 1 is paired with two different outputs.

Question 12

If $$f(x) = 3x - 7$$, what is $$f(4)$$?

Accepted Answer

$$5$$

Question 13

Which of the following is the correct interpretation of $$f(2x)$$ for a function $$f$$?

Accepted Answer

Evaluate $$f at$$ $$2x by $$replacing every $$x in$$ $$f(x)$$ with $$2x.$$

Question 14

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

Accepted Answer

$$[1, \infty)$$

Question 15

If $$f(x) = x^2$ and g(x) = x + 1$, what is $$\left(\dfrac{f}{g}\right)(x)$$?

Accepted Answer

$$\dfrac{x^2$}{x+1}$$

Question 16

A function $$f is $$defined by $$f(x) = \dfrac{1}{x^2$ - 9}. $$What is the domain of $$f$$?

Accepted Answer

$$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$

Question 17

If $$f(x) = x^2$ + 2x + 1$$, what is $$f(x+h) - f(x)$$?

Accepted Answer

$$2xh + h^2$ + 2h$$

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

$$[0, \infty)$$

Functions and Their Graphs: Foundations of Precalculus

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