$$\dfrac{x^2$}{x - 2}$$, domain: $$x \neq 2$$

Question 1

Which of the following best describes the difference between a relation and a function?

Accepted Answer

A function is a relation in which each input is assigned to exactly one output.

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

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

Accepted Answer

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

Question 4

If $$f(x) = 2x^2$ - 5x$$, what is $$f(-x)$$?

Accepted Answer

$$2x^2 + 5x$

Question 5

Given $$f(x) = x^2$ + 1$$, what is the domain of $$f$$?

Accepted Answer

All real numbers

Question 6

Let $$g(x) = \dfrac{x}{x^2$ - 25}. $$What is the domain of $$g$$?

Accepted Answer

$$x 
eq 5$$ and $$x 
eq -5$$

Question 7

If $$h(t) = \sqrt{5 - 5t}$$, for which values of $$t is$$ $$h(t)$$ defined?

Accepted Answer

$$t \leq 1$$

Question 8

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

Accepted Answer

$$V(s) = s^3$, domain: s$$ \u003e 0$$

Question 9

Given $$f(x) = 2x^2$ - 5x$$, what is $$f(x + 2)$$?

Accepted Answer

$$2x^2 + 3x - 2$

Question 10

Which of the following is the correct formula for the difference quotient of a function $$f$$?

Accepted Answer

$$\dfrac{f(x + h) - f(x)}{h}$$

Question 11

Let $$f(x) = \dfrac{1}{x + 3}$$ and $$g(x) = \dfrac{1}{x - 4}. $$What is the domain of $$f(x) + g(x)$$?

Accepted Answer

$$x 
eq -3$$ and $$x 
eq 4$$

Question 12

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

Accepted Answer

$$x \geq 0$$

Question 13

Which of the following statements is TRUE about the range of a function?

Accepted Answer

The range is the set of all possible outputs for the function.

Question 14

Given $$f(x) = 2x^2$ - 5x$$, what is $$2f(x)$$?

Accepted Answer

$$4x^2 - 10x$

Question 15

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

Accepted Answer

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

Question 16

Which of the following best describes function notation?

Accepted Answer

It expresses the output as a function of the input, such as $$y = f(x).$$

Question 17

Suppose $$f(x) = x^2$ and g(x) = x - 2$. What is $$\left(\dfrac{f}{g}\right)(x)$$ and its domain?

Accepted Answer

$$\dfrac{x^2$}{x - 2}$$, domain: $$x 
eq 2$$

Question 18

Which of the following is an example of a function given implicitly?

Accepted Answer

$$2x + y = 4$$

Question 19

If $$f(x) = 2x^2$ - 5x$$, what is $$f(x) + f(2)$$?

Accepted Answer

$$2x^2 - 5x - 2$

Functions and Their Graphs: Foundations and Operations

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