Question 1

Which of the following best describes a function?

Accepted Answer

A correspondence where each member of the domain corresponds to exactly one member of the range.

Question 2

Given the function $$f(x) = 3x + 5$$, what is $$f(-5)$$?

Accepted Answer

$$-10$$

Question 3

Which of the following correspondences is NOT a function?

Accepted Answer

Assigning each city to its basketball team, where one city has two teams.

Question 4

If $$f(x) = x^2$, what is f(x+h$$)$$ in terms of x$ and h$?

Accepted Answer

$$x^2 + 2xh$$ + $$h^2$$

Question 5

A function $$f is $$defined as $$f(x) = x - x^2$. What is f(4$$)$$?

Accepted Answer

$$-12$$

Question 6

Which of the following graphs passes the vertical-line test?

Accepted Answer

A graph where no vertical line intersects the graph more than once.

Question 7

Given $$f(x) = 2x - x^2$, find $$\frac{f(x+h) - f(x)}{h}$$ and simplify.

Accepted Answer

$$2 - 2x - h$$

Question 8

Which of the following is the correct graph for the piecewise function $$g(x) = \begin{cases} 3, & x = 1 \ -x + 2, & x 
eq 1 \end{cases}$$?

Accepted Answer

A line $$y = -x + 2$$ with an open circle at $$(1, 1)$$ and a filled dot at $$(1, 3).$$

Question 9

If $$f(x) = x^2$ - 1$$, what is the $$y-$$intercept of its graph?

Accepted Answer

$$-1$$

Question 10

Suppose a function $$f is $$defined by $$f(x) = 2 - x$$ for $$x 
eq -2$$ and $$f(-2) = 1. $$What is $$f(0)$$?

Accepted Answer

$$2$$

Question 11

Which of the following real-world scenarios is best modeled by a function?

Accepted Answer

Assigning each person in a city to their unique social security number.

Question 12

Given $$f(x) = x - x^2$, what is $$\frac{f(x+h) - f(x)}{h}$$ simplified?

Accepted Answer

$$1 - 2x - h$$

Question 13

Which of the following is NOT a property of a function?

Accepted Answer

Each input can correspond to multiple outputs.

Question 14

If $$f(x) = x^2$, what is f$$(\sqrt{k})$$?

Accepted Answer

$$k$$

Question 15

Which of the following best describes the vertical-line test?

Accepted Answer

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

Question 16

Given $$f(x) = 3x + 5$$, what is $$f(x+h)$$?

Accepted Answer

$$3x + 3h + 5$$

Question 17

Which of the following is the correct process for graphing $$f(x) = x^2$ - 1$$?

Accepted Answer

Choose values for $$x$$, compute $$f(x)$$, plot $$(x, f(x))$$, and connect the points.

Question 18

If $$f(x) = x^2$, which of the following is true?

Accepted Answer

Two different inputs can have the same output.

Question 19

Given the piecewise function $$f(x) = \begin{cases} 1, & x = -2 \ 2 - x, & x 
eq -2 \end{cases}$$, what is $$f(-2)$$?

Accepted Answer

$$1$$

Question 20

Which of the following is a valid reason why the correspondence 'city to basketball team' is not a function in some cases?

Accepted Answer

A city can have more than one basketball team.

Functions and Models: Foundations for Calculus

Study Guide - Practice Questions