Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each element in the domain is paired with exactly one element in the range.

Question 2

Given the function $$f(x) = \frac{x+1}{x+2}$$, what is the domain of $$f$$?

Accepted Answer

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

Question 3

Which of the following equations is an explicit form of a function?

Accepted Answer

$$y = f(x) = x^2$ - 6$$

Question 4

For the function $$f(x) = \sqrt{9 - x}$$, what is the domain?

Accepted Answer

$$(-\infty, 9]$$

Question 5

What is the difference quotient for $$f(x) = x^2$ + 2x$$?

Accepted Answer

$$2x + h + 2$$

Question 6

If $$f(x) is an $$even function, which of the following must be true?

Accepted Answer

$$f(-x) = f(x)$$

Question 7

Which of the following statements is true about the graph of an odd function?

Accepted Answer

It is symmetric with respect to the origin.

Question 8

Given the graph of $$y = f(x)$$ with points $$(-1, 1)$$, $$(1, 2)$$, and $$(3, 0)$$, what is the local maximum value?

Accepted Answer

$$2$$

Question 9

Suppose $$f(x) is $$defined and continuous on $$[a, b]. $$According to the Extreme Value Theorem, what can be concluded?

Accepted Answer

$$f(x)$$ attains both an absolute maximum and minimum on $$[a, b]$$

Question 10

For the function $$f(x) = \frac{10}{3x}$$, what value(s) of $$x$$ must be excluded from the domain?

Accepted Answer

$$x = 0$$

Question 11

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

Accepted Answer

For any $$x_1$$ \u003c $$x_2 in$$ $$I$$, $$f(x_1$) \u003c f(x_2$)$$

Question 12

Given the function $$f(x) = x^2$ + 7x + 5$$, is $$f$$ even, odd, or neither?

Accepted Answer

Neither

Question 13

If $$f(x) = x^5$ - 4x$$, determine whether $$f is $$even, odd, or neither.

Accepted Answer

Odd

Question 14

A function $$f$$ has a local minimum at $$x = 3 if$$:

Accepted Answer

$$f(3) \leq f(x)$$ for all $$x in an $$open interval containing $$3$$

Question 15

Consider the scenario: Barbara walks 2 blocks in 5 minutes, runs home in 1 minute, spends 1 minute at home, walks 5 blocks in 15 minutes, and jogs home in 7 minutes. Which segment of her distance-time graph has the steepest negative slope?

Accepted Answer

Jogging home in 7 minutes

Question 16

Given the graph of $$y = f(x)$$ with labeled points $$(-10, 0)$$, $$(-8, -4)$$, $$(-2, 6)$$, $$(2, 10)$$, $$(5, 0)$$, and $$(7, 3)$$, what is the absolute maximum value of $$f on$$ $$[-10, 7]$$?

Accepted Answer

$$10$$

Question 17

For the function $$f(x) = \frac{x+1}{x+2}$$, what is the $$x-$$intercept?

Accepted Answer

$$x = -1$$

Question 18

If $$f(x) is $$constant on an interval $$I$$, what can be said about $$f(x_1$)$$ and $$f(x_2$)$$ for any $$x_1$$, $$x_2 in$$ $$I$$?

Accepted Answer

$$f(x_1$) = f(x_2$)$$

Question 19

Given the graph of $$y = f(x)$$ with points $$(0, 4)$$, $$(\pi, -4)$$, $$(2\pi, 4)$$, and $$(3\pi, -4)$$, what is the range of $$f$$?

Accepted Answer

$$[-4, 4]$$

Functions: Definitions, Properties, and Graphical Analysis

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