Question 1

Given the graph in $$image_1$$, what is the domain of the function?

Accepted Answer

$$(-\infty, -4] \cup (-4, 2] \cup (3, \infty)$$

Question 2

Given the graph in $$image_1$$, what is the range of the function?

Accepted Answer

$$(-\infty, 8) \cup (2, \infty)$$

Question 3

Which of the following functions is even?

Accepted Answer

$$f(x) = x^4$ - 2x^2$ - 3$$

Question 4

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ - 4x$$

Question 5

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

Accepted Answer

$$2x + h - 2$$

Question 6

Which of the following statements is true about the symmetry of the ellipse shown in $$image_5$$?

Accepted Answer

It is symmetric about both the x-axis and y-axis.

Question 7

Given the piecewise function in $$image_12$$, what is the value of the function at $$x = 0$$?

Accepted Answer

2

Question 8

Which of the following best describes the intervals where the function $$f(x) = x^3$ - 4x is $$increasing?

Accepted Answer

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

Question 9

Which test would you use to determine if a function is symmetric about the origin?

Accepted Answer

Check if $$f(-x) = -f(x)$$ for all $$x in $$the domain.

Question 10

Which of the following is NOT a function?

Accepted Answer

A relation where one input has two different outputs.

Question 11

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

Accepted Answer

$$2(x+h)^2 - (x+h) + 3$

Question 12

Which of the following best describes an absolute maximum?

Accepted Answer

The highest $$y-$$value over the entire domain of the function.

Question 13

If a function is constant on an interval, what can you say about its rate of change on that interval?

Accepted Answer

The rate of change is zero.

Question 14

Which of the following is true about the difference quotient for a linear function $$f(x) = mx + b$$?

Accepted Answer

It is always equal to the slope $$m.$$

Question 15

Which of the following is a necessary condition for a function to be classified as even?

Accepted Answer

$$f(-x) = f(x)$$ for all $$x in $$the domain.

Question 16

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$2x + h$$

Question 17

A function $$f is $$defined on $$[2, 16]$$ and its graph is shown in $$image_8. $$What is the range of $$f$$?

Accepted Answer

$$[2, 10]$$

Question 18

Which of the following is true about the graph of $$y^2 = 4px$ (see $$image_2$$)?

Accepted Answer

It is symmetric about the y-axis.

Question 19

Which of the following is a real-world example of a piecewise function?

Accepted Answer

A taxi fare that charges a flat rate for the first mile and a different rate for each additional mile.

Key Concepts in Functions: Symmetry, Increasing/Decreasing Intervals, and the Difference Quotient

Study Guide - Practice Questions