Question 1

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

Accepted Answer

$$(-\infty, 0)$$

Question 2

Which of the following best describes the symmetry of the function $$f(x) = x^3$?

Accepted Answer

Odd; symmetric with respect to the origin

Question 3

A function $$f is $$defined as $$f(x) = \begin{cases} 2 & x \u003c 0 \ x-1 & x \geq 0 \end{cases}. $$What is $$f(-3)$$?

Accepted Answer

$$2$$

Question 4

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

Accepted Answer

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

Question 5

If $$f(x) = x^2$ - 2$$, what is the relative minimum value of $$f$$?

Accepted Answer

$$-2$$

Question 6

Which of the following statements is true for an even function $$f$$?

Accepted Answer

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

Question 7

Given the piecewise function $$f(x) = \begin{cases} 3 & x \u003c 1 \ x^2$ & x \geq 1 \end{cases}$$, what is $$f(2)$$?

Accepted Answer

$$4$$

Question 8

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 9

A function $$f is $$constant on the interval $$[a, b] if$$:

Accepted Answer

$$f(x_1$) = f(x_2$)$$ for all $$x_1$$, $$x_2 in$$ $$[a, b]$$

Question 10

Suppose $$f(x) = x^2$ - 2. $$Find and simplify the difference quotient $$\dfrac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$2x + h$$

Question 11

Which of the following best describes the graph of $$f(x) = |x|$$?

Accepted Answer

It is symmetric with respect to the y-axis

Question 12

A function $$f$$ has a relative maximum at $$x = 2 if$$:

Accepted Answer

$$f(2) \u003e f(x)$$ for all $$x$$ near $$2$$

Question 13

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

Accepted Answer

The graph is symmetric with respect to the y-axis

Question 14

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

Accepted Answer

$$2$$

Question 15

Which of the following real-world scenarios best models 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

Question 16

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

Accepted Answer

$$f(-x) = f(x)$$ for all $$x$$

Question 17

Which of the following intervals describes where the function $$f(x) = -x^2$ is increasing?

Accepted Answer

$$(0, \infty)$$

Question 18

Suppose $$f(x) = x^2$ - 2. $$What is the value of the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$ when $$x = 1$$ and $$h = 2$$?

Accepted Answer

$$4$$

Question 19

Which of the following is a necessary condition for a function to be constant on an interval?

Accepted Answer

The function's graph is a horizontal line on that interval

Functions and Their Graphs: Key Concepts and Applications

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