Question 1

Which of the following best describes the relation shown in the table where time (in seconds) is paired with height (in meters) for a rock thrown on the Moon?

Accepted Answer

A numerical description of a relation

Question 2

Given the relation represented by the set of ordered pairs $$\{(0, 3), (-1, 4), (0, 5), (3, 0)\}$$, what is the domain and range?

Accepted Answer

Domain: $$\{0, -1, 3\}$$, Range: $$\{3, 4, 5, 0\}$$

Question 3

Which of the following equations does NOT represent a function?

Accepted Answer

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

Question 4

Consider the mapping diagram where each person is paired with their birthday. Which property makes this a function?

Accepted Answer

Each person is paired with exactly one birthday.

Question 5

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

Accepted Answer

$$4$$

Question 6

What is the domain of the function $$f(x) = \sqrt{x - 1}$$?

Accepted Answer

$$[1, \infty)$$

Question 7

For the rational function $$f(x) = \frac{x+2}{x-4}$$, which value must be excluded from the domain?

Accepted Answer

$$x = 4$$

Question 8

If $$f(x) = \frac{x+3}{x+4}$$, what is the $$x-$$intercept of the function?

Accepted Answer

$$x = -3$$

Question 9

Given the graph of $$y = x^2$, which transformation results in the graph of y$$ = $$x^2 + 3$?

Accepted Answer

A vertical shift up by 3 units

Question 10

Which parent function matches the graph of $$y = |x|$$?

Accepted Answer

Absolute value function

Question 11

For the function $$f(x) = \sqrt{2x - 3}$$, what is the domain?

Accepted Answer

$$\left[\frac{3}{2}, \infty\right)$$

Question 12

Which of the following describes a vertical compression of the graph of $$y = f(x)$$?

Accepted Answer

$$y = 0.5f(x)$$

Question 13

If $$f(x) = x^2$, which equation represents a reflection of f(x$$)$$ over the y$-axis?

Accepted Answer

$$f(-x) = (-x)^2$

Question 14

Given the graph of a function, how do you determine where the function is positive?

Accepted Answer

Where the graph is above the $$x-$$axis

Question 15

Which of the following is the parent function for $$g(x) = 2\sqrt{x} + 1$$?

Accepted Answer

$$f(x) = \sqrt{x}$$

Question 16

If $$f(x) = x^2$ and g(x) = f(x-2) + 1$, what transformations have been applied to the parent function?

Accepted Answer

Shift right 2 units, shift up 1 unit

Question 17

Which of the following is NOT a function?

Accepted Answer

A circle defined by $$x^2$$ + $$y^2 = 1$

Question 18

Given the function $$f(x) = \frac{x}{x+6}$$, what is the domain?

Accepted Answer

$$(-\infty, -6) \cup (-6, \infty)$$

Question 19

If $$f(x) = |x|$$, what is the effect of the transformation $$g(x) = |x| + 5$$?

Accepted Answer

The graph shifts up 5 units

Question 20

Which of the following best describes the range of the parent function $$f(x) = x^2$?

Accepted Answer

$$[0, \infty)$$

College Algebra: Functions and Their Graphs – Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards