Question 1

Which of the following best describes the symmetry of the graph shown in the first image?

Accepted Answer

The graph is symmetric with respect to the origin.

Question 2

Given the function $$f(x) = x^3$ - 6x$$, determine whether it is even, odd, or neither.

Accepted Answer

Odd

Question 3

Which of the following functions is NOT a function according to the vertical line test?

Accepted Answer

$$x = y^2$ - 1$$

Question 4

What is the domain of the function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 5

For the piecewise function $$f(x) = \begin{cases} x+2 & x \leq 1 \ 4 & x \u003e 1 \end{cases}$$, what is $$f(10)$$?

Accepted Answer

$$4$$

Question 6

Which of the following best describes the behavior of the function $$f(x) = x^2$?

Accepted Answer

Decreasing on $$(-\infty, 0)$$ and increasing on $$(0, \infty)$$

Question 7

Find the difference quotient for $$f(x) = 2x^2$ - x + 3.$$

Accepted Answer

$$4x + 2h - 1$$

Question 8

Which of the following statements is TRUE about even and odd functions?

Accepted Answer

Even functions are symmetric with respect to the y-axis.

Question 9

Given the function $$f(x) = |x|$$, which of the following best describes its symmetry?

Accepted Answer

Symmetric with respect to the y-axis

Question 10

A company’s profit $$P(x) in $$thousands of dollars is modeled by $$P(x) = -2x^2$ + 8x + 3$$, where $$x is $$the number of units sold in thousands. What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$11$$ thousand dollars at $$x = 2$$ thousand units.

Question 11

Which of the following is the range of the function $$f(x) = x^2$ - 1$$?

Accepted Answer

$$[-1, \infty)$$

Question 12

Suppose $$f(x) is a $$function such that $$f(-x) = -f(x)$$ for all $$x in $$its domain. Which of the following must be true?

Accepted Answer

$$f(x) is an $$odd function.

Question 13

Which of the following real-world scenarios can be best modeled by 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 14

Given the graph in the fifth image, which of the following statements is true about the function shown?

Accepted Answer

The function has a relative maximum at $$x \approx 2$$ and a relative minimum at $$x \approx 4.$$

Question 15

If a function passes the vertical line test, which of the following must be true?

Accepted Answer

Each $$x-$$value is paired with exactly one $$y-$$value.

Graphs and Properties of Functions in College Algebra

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