Question 1

Which of the following relations is NOT a function?

Accepted Answer

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

Question 2

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

Accepted Answer

$$11$$

Question 3

Which equation does NOT represent $$y as a $$function of $$x$$?

Accepted Answer

$$y^2 = x$

Question 4

A vertical line on a graph fails the vertical line test. What does this indicate?

Accepted Answer

The graph does not represent a function.

Question 5

If $$f(x) = 3x + 7$$, what is $$f(x+1)$$?

Accepted Answer

$$3x + 10$$

Question 6

Given $$g(x) = x^2$ - 10x - 3$$, what is $$g(-x)$$?

Accepted Answer

$$x^2 + 10x - 3$

Question 7

Which of the following best describes the domain of $$y = x^2$?

Accepted Answer

$$(-\infty, \infty)$$

Question 8

A chemical reaction is modeled by $$f(t) = 5t - 2$$, where $$t is $$time in seconds. What is the output after 3 seconds?

Accepted Answer

$$13$$

Question 9

Given $$f(x) = \frac{4x^3$ + 1}{x^3$}$$, what is $$f(-2)$$?

Accepted Answer

$$\frac{31}{-8}$$

Question 10

Which of the following statements about functions is TRUE?

Accepted Answer

A function assigns exactly one output to each input.

Question 11

If $$f(x) = x - 4$$ and $$g(x) = x$$, how does the graph of $$f(x)$$ relate to $$g(x)$$?

Accepted Answer

It is shifted 4 units down.

Question 12

A medical dosage is modeled by $$d(x) = 2x + 5$$, where $$x is $$the number of hours since administration. What is the dosage after 6 hours?

Accepted Answer

$$17$$

Question 13

Given the set $$\{(4,1), (5,1), (6,1)\}$$, is this a function?

Accepted Answer

Yes, because each x-value has only one y-value.

Question 14

If $$f(x) = x^2$, what is the range of f(x$$)$$?

Accepted Answer

$$[0, \infty)$$

Question 15

Which of the following equations is a function of $$x$$?

Accepted Answer

$$x + y = 25$$

Question 16

A population model is given by $$P(t) = 1000e$$^{0.05t}$$, where t$ is years. What is P(0$$)$$?

Accepted Answer

$$1000$$

Question 17

If $$f(x) = x^2$ - 4x + 3$$, what is the y-intercept of the graph?

Accepted Answer

$$3$$

Question 18

Which of the following describes the range of $$f(x) = x^2$ + 4$$?

Accepted Answer

$$[4, \infty)$$

Question 19

If a graph passes the vertical line test everywhere, what does this mean?

Accepted Answer

The graph represents a function.

Question 20

Given $$f(x) = x^2$ - 6x + 9$$, what is $$f(3)$$?

Accepted Answer

$$0$$

2.1 Functions and Their Graphs: College Algebra Study Notes

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