Question 1

Which of the following best describes when a function $$f(x) is $$said to be increasing on an interval $$I$$?

Accepted Answer

$$f(x_1$) \u003c f(x_2$)$$ for any $$x_1$$ \u003c $$x_2 in I$$

Question 2

Given the function $$f(x) = x^2$ - 4x + 3$$, on which interval is the function decreasing?

Accepted Answer

$$(2, \infty)$$

Question 3

A function $$f$$ has a relative maximum at $$x = a if$$:

Accepted Answer

$$f(a) \geq f(x)$$ for all x$$ in an open interval containing a$

Question 4

Which test would you use to determine if the graph of $$y = f(x) is $$symmetric with respect to the y-axis?

Accepted Answer

Replace $$x$$ with $$-x$$ and check if the equation is unchanged

Question 5

Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$ + 1$$

Question 6

Which of the following statements is true for an odd function $$f(x)$$?

Accepted Answer

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

Question 7

Given the piecewise function $$f(x) = \begin{cases} x+2 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$-1$$

Question 8

Given the piecewise function $$f(x) = \begin{cases} 2x & x \u003c 1 \ x^2$ & x \geq 1 \end{cases}$$, what is $$f(2)$$?

Accepted Answer

$$4$$

Question 9

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

Accepted Answer

$$\frac{(x+h)^2$ - x^2$}{h}$$

Question 10

Simplify the difference quotient for $$f(x) = 3x + 2.$$

Accepted Answer

$$3$$

Question 11

If $$f(x) = x^2$ - 1$$, what is the simplified form of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h$$

Question 12

Which of the following functions is neither even nor odd?

Accepted Answer

$$f(x) = x^2$ + x$$

Question 13

A function $$f is $$constant on an interval $$I if$$:

Accepted Answer

$$f(x_1$) = f(x_2$)$$ for any $$x_1$$, $$x_2 in I$$

Question 14

Which of the following real-world scenarios best models a piecewise function?

Accepted Answer

A taxi fare that charges $$5 for the first mile and 2 $$for each additional mile

Question 15

If $$f(x) = |x|$$, which of the following statements is true?

Accepted Answer

$$f(x) is $$even

Question 16

Suppose $$f(x) is $$decreasing on $$(-\infty, 0)$$ and increasing on $$(0, \infty). $$What can you conclude about $$x = 0$$?

Accepted Answer

$$x = 0 is a $$relative minimum

Functions and Their Graphs: Key Concepts and Applications

Study Guide - Practice Questions