Question 1

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{ (1,2), (3,4), (6,5), (8,5) \}$$

Question 2

Given the piecewise function for shipping cost $$C(w)$$:

$$C(w) = \begin{cases} 5.00 & 	ext{if } 0  5 \end{cases}$$

What is the cost to ship a package weighing $$4$$ units?

Accepted Answer

$$8.00$$

Question 3

Which of the following best describes the domain of the function $$f(x) = \sqrt{9x - 27}$$?

Accepted Answer

$$x \geq 3$$

Question 4

If $$f(x) = x^2$ and g(x) = x + 3$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = f(5) = 25$$

Question 5

Which of the following is NOT a valid reason for a value to be excluded from a function's domain?

Accepted Answer

The value makes the function output a negative number.

Question 6

A function $$f is $$said to be even if:

Accepted Answer

$$f(-x) = f(x)$$ for all x in the domain

Question 7

Which transformation will reflect the graph of $$y = f(x)$$ across the y-axis?

Accepted Answer

$$y = f(-x)$$

Question 8

Suppose $$f(x) is $$increasing on the interval $$(-\infty, 2)$$ and decreasing on $$(2, \infty). $$What can you conclude about $$x = 2$$?

Accepted Answer

$$x = 2 is a $$relative maximum

Question 9

Given $$f(x) = x^2$ and g(x) = x - 1$, what is the domain of $$\left(\frac{f}{g}\right)(x)$$?

Accepted Answer

$$x 
eq 1$$

Question 10

Which of the following describes a vertical stretch of the graph $$y = f(x) by a $$factor of $$3$$?

Accepted Answer

$$y = 3f(x)$$

Question 11

If $$f(x) = x^3$, which of the following statements is true?

Accepted Answer

$$f(x) is an $$odd function

Question 12

Which of the following is the correct order for performing multiple transformations on a function?

Accepted Answer

Horizontal shifting, stretching/shrinking, reflecting, vertical shifting

Question 13

Which of the following is the sum of $$f(x) = 2x$$ and $$g(x) = x^2$?

Accepted Answer

$$2x + x^2$

Question 14

A function $$f is $$decreasing on the interval $$(1, 4). $$Which of the following best describes the behavior of $$f(x) as$$ $$x$$ increases from $$1 to$$ $$4$$?

Accepted Answer

$$f(x)$$ decreases$

Question 15

Which of the following is the correct formula for the product of two functions $$f$$ and $$g$$?

Accepted Answer

$$(f \cdot g)(x) = f(x) \cdot g(x)$$

Question 16

If $$f(x) = x^2$ and g(x) = x + 3$, what is (g$$ \circ f)(1)$$?

Accepted Answer

$$g(f(1)) = g(1^2$) = g(1) = 4$$

Question 17

Which of the following is a real-world example of a piecewise function?

Accepted Answer

The cost of shipping a package based on its weight, where different weight intervals have different costs

Functions and Their Properties: Definitions, Operations, and Transformations

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