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 function, because each time value corresponds to exactly one height value.

Question 2

Given the relation $$\{(0, 3), (-1, 4), (0, 5), (3, 0)\}$$, 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

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

Accepted Answer

$$4$$

Question 5

What is the domain of the function $$f(x) = \sqrt{x - 5}$$?

Accepted Answer

$$[5, \infty)$$

Question 6

For the function $$f(x) = \frac{x+3}{x+4}$$, what value(s) must be excluded from the domain?

Accepted Answer

$$x = -4$$

Question 7

If $$f(x) = |x| + 5$$, which transformation has been applied to the parent function $$f(x) = |x|$$?

Accepted Answer

A vertical shift up by 5 units.

Question 8

Which of the following is the parent function for $$g(x) = 2x^2$ - 1$$?

Accepted Answer

$$f(x) = x^2$

Question 9

Given the graph of $$y = x^2$, which transformation results in the graph of y$$ = $$x^2 - 4$?

Accepted Answer

A vertical shift down by 4 units.

Question 10

Suppose a function $$f(x) is $$positive for $$x in $$the interval $$(1, 4)$$ and negative for $$x in $$the interval $$(-2, 1). $$Which statement is true?

Accepted Answer

$$f(x) \u003e 0$$ for $$1 \u003c x \u003c 4$$

Question 11

Which of the following describes a vertical stretch of the parent function $$f(x) = \sqrt{x} by a $$factor of 2?

Accepted Answer

$$f(x) = 2\sqrt{x}$$

Question 12

If $$f(x) = x^2$, what is the effect of the transformation f(-x$$)$$ on the graph?

Accepted Answer

Reflection over the y-axis.

Question 13

Given the function $$f(x) = \frac{x}{x-2}$$, what is the y-intercept?

Accepted Answer

$$(0, 0)$$

Question 14

Which of the following is the domain of the function $$f(x) = \sqrt{3x + 4}$$?

Accepted Answer

$$\left[ -\frac{4}{3}, \infty \right)$$

Question 15

Which of the following graphs represents a relation that is NOT a function?

Accepted Answer

A circle centered at the origin.

Question 16

If $$f(x) = x^2$, what is 4f(-2x$$)$$?

Accepted Answer

$$16x^2$$

Question 17

Which of the following is the correct interval notation for all real numbers except $$x = 2$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 18

Given the function $$f(x) = \frac{x+2}{x-1}$$, for which value of $$x is $$the function undefined?

Accepted Answer

$$x = 1$$

Question 19

Which transformation will reflect the graph of $$f(x)$$ over the x-axis?

Accepted Answer

$$y = -f(x)$$

College Algebra Study Guide: Functions and Their Graphs

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