Question 1

Which of the following best describes a function?

Accepted Answer

A rule that assigns to each element $$x in a $$set $$A$$ exactly one element, called $$f(x)$$, in a set $$B.$$

Question 2

Which of the following is NOT a valid way to represent a function?

Accepted Answer

Using a random list of numbers with no relationship.

Question 3

A company charges a flat fee of $$\50$ for a service, regardless of the number of hours worked. Which type of function best models this situation?

Accepted Answer

A constant function $$f(x) = 50$$

Question 4

Given the function $$f(x) = 2x + 3$$, what is the $$y-$$intercept of its graph?

Accepted Answer

$$3$$

Question 5

Which of the following graphs does NOT represent a function?

Accepted Answer

A circle centered at the origin

Question 6

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, which of the following statements is true about their domains?

Accepted Answer

The domain of $$f(x) is $$all real numbers, while the domain of $$g(x) is$$ $$[0, \infty).$$

Question 7

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

Accepted Answer

$$f(x_1$) \u003c f(x_2$)$$ whenever $$x_1$$ \u003c $$x_2 in$$ $$I$$

Question 8

Suppose the graph of $$f(x)$$ passes the vertical line test. What does this imply?

Accepted Answer

Each input $$x$$ has exactly one output $$f(x)$$, so $$f is a $$function.

Question 9

Given $$f(x) = 2x^2$ + 3$$ and $$g(x) = 5x + 6$$, for which values of $$x do $$the graphs of $$f$$ and $$g$$ intersect?

Accepted Answer

$$x = -0.5$$ and $$x = 3$$

Question 10

For the function $$f(x) = \sqrt{4 - x^2$}$$, what is the domain?

Accepted Answer

$$[-2, 2]$$

Question 11

If $$f(x) = 12x^3$ + 4x - 3x^2$, which of the following statements is true about its increasing and decreasing intervals?

Accepted Answer

$$f is $$increasing on $$(-\infty, -1]$$ and $$[2, \infty)$$, and decreasing on $$[-1, 0]$$ and $$[0, 2]$$

Question 12

A local maximum value of a function $$f at$$ $$x = a$$ means:

Accepted Answer

$$f(a) \geq f(x)$$ for all $$x$$ near $$a$$

Question 13

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

Accepted Answer

The area $$A of a $$circle as a function of its radius $$r$$, $$A(r) = \pi r^2$

Question 14

If the solution to $$f(x) \u003c g(x) is $$the interval $$[-0.5, 3]$$, what does this mean graphically?

Accepted Answer

The graph of $$f(x)$$ lies below the graph of $$g(x)$$ for $$x in$$ $$[-0.5, 3]$$

Question 15

Which of the following is a root function?

Accepted Answer

$$f(x) = x$$^{1/2}$$

Question 16

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

Accepted Answer

$$f(x_1$) \u003e f(x_2$)$$ whenever $$x_1$$ \u003c $$x_2 in$$ $$I$$

Question 17

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

Accepted Answer

$$[0, \infty)$$

Question 18

If a function $$f is $$defined by the rule 'square the number', which of the following is the correct formula?

Accepted Answer

$$f(x) = x^2$

Question 19

A local minimum value of a function $$f at$$ $$x = a$$ means:

Accepted Answer

$$f(a) \leq f(x)$$ for all $$x$$ near $$a$$

Functions and Their Graphs: College Algebra Study Notes

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