Question 1

Given the relation $$\{(2, 5), (3, 7), (2, 8), (4, 9)\}$$, what is the domain of the relation?

Accepted Answer

$$\{2, 3, 4\}$$

Question 2

Which of the following relations is a function?

Accepted Answer

$$\{(0, 1), (1, 2), (2, 3)\}$$

Question 3

Given the equation $$x^2$$ + $$y^2 = 9$, does this equation define y$ as a function of x$?

Accepted Answer

No, because for some $$x$$ values there are two corresponding $$y$$ values.

Question 4

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

Accepted Answer

$$f(-2) = 15$$

Question 5

Which of the following best describes the vertical line test?

Accepted Answer

If any vertical line touches the graph at more than one point, the graph is not a function.

Question 6

Given the graph of $$y = f(x)$$, which of the following statements is true about the y-intercept?

Accepted Answer

The y-intercept is the point where $$x = 0.$$

Question 7

A function $$g(x) is $$defined for all real numbers except $$x = 2. $$What is the domain of $$g(x)$$?

Accepted Answer

$$\{x \mid x 
eq 2\}$$

Question 8

Suppose the graph of a function passes through the points $$(-3, 0)$$, $$(-1, 0)$$, and $$(2, 0). $$What are the x-intercepts?

Accepted Answer

$$x = -3, -1, 2$$

Question 9

If the range of a function $$h is$$ $$\{2, 4, 6, 8\}$$, which of the following could be a possible set of ordered pairs for $$h$$?

Accepted Answer

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

Question 10

A real-world scenario: The temperature $$T (in $$degrees Celsius) at hour $$h is $$given by $$T(h) = 20 - 2h. $$What is the temperature at 5 hours?

Accepted Answer

$$T(5) = 10$$

Question 11

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

Accepted Answer

$$x = y^2$

Question 12

Given the function $$f(x) = 3x - 4$$, what is the y-intercept of its graph?

Accepted Answer

$$-4$$

Question 13

If a function $$f$$ has domain $$\{0, 1, 2, 3\}$$ and range $$\{5, 6, 7, 8\}$$, which of the following is a possible value for $$f(2)$$?

Accepted Answer

$$5$$

Question 14

A function $$f is $$graphed and passes the vertical line test. Which of the following must be true?

Accepted Answer

For every $$x in $$the domain, there is exactly one $$y$$ value.

Question 15

Given the function $$f(x) = x^2$ - 4x + 3$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1 or$$ $$x = 4$$

Question 16

Which of the following best describes the range of the function $$f(x) = x^2$ for x$ in $$\mathbb{R}$$?

Accepted Answer

$$\{x \mid x \geq 0\}$$

Functions and Their Graphs: Foundations and Analysis

Study Guide - Practice Questions