Question 1

Which of the following best describes a function?

Accepted Answer

A correspondence between two sets where each element of the domain is paired with exactly one element of the range.

Question 2

Given the function $$f(x) = x^2$, what is the value of f(3$$)$$?

Accepted Answer

$$9$$

Question 3

If $$f(x) = x^2$, what is the value of $$\frac{f(3+h) - f(3)}{h}$$ for h$$ 
eq 0$$?

Accepted Answer

$$6 + h$$

Question 4

Which of the following graphs passes the vertical-line test and therefore represents a function?

Accepted Answer

A graph where every vertical line intersects the curve at most once.

Question 5

Consider the function $$g(x)$$ defined as $$g(x) = \begin{cases} x, & 	ext{for } x = 1 \ x + 2, & 	ext{for } x 
eq 1 \end{cases}. $$What is $$g(1)$$?

Accepted Answer

$$1$$

Question 6

Which statement about the domain and range of a function is correct?

Accepted Answer

The domain is the set of all possible inputs, and the range is the set of all possible outputs.

Question 7

Given the function $$f(x) = 2x + 3$$, which ordered pair is on the graph of $$f$$?

Accepted Answer

$$(2, 7)$$

Question 8

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

Accepted Answer

The graph does not represent a function.

Question 9

If $$f(x) = x^2$ and x$ represents the number of hours a machine runs, what does f(5$$)$$ represent in a real-world context?

Accepted Answer

The square of the number of hours the machine runs, which could represent total energy used if energy is proportional to time squared.

Question 10

Which of the following is NOT a function?

Accepted Answer

A rule that assigns some inputs to more than one output.

Question 11

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

Accepted Answer

$$25$$

Question 12

If a graph of $$y = f(x) is $$given, what does the point $$(a, f(a))$$ represent?

Accepted Answer

The input $$a$$ and its corresponding output $$f(a).$$

Question 13

Which of the following best describes the dependent variable in a function?

Accepted Answer

The variable that represents the output.

Question 14

Suppose $$f(x) = 2x + 3. If $$the input increases from $$x = 1 to$$ $$x = 4$$, what is the change in the output?

Accepted Answer

$$6$$

Question 15

A hospital uses the function $$f(x) = x^2$ to estimate the cost of a procedure based on the number of hours x$ it takes. If the procedure takes 4 hours, what is the estimated cost?

Accepted Answer

$$16$$

Question 16

Which of the following ordered pairs is NOT on the graph of $$y = 2x + 3$$?

Accepted Answer

$$(3, 8)$$

Question 17

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

Accepted Answer

$$6$$

Question 18

Which of the following statements is true about the vertical-line test?

Accepted Answer

A graph represents a function if no vertical line intersects the graph more than once.

Functions: Definitions, Evaluation, and Graphs

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