Question 1

Which of the following equations represents a function?

Accepted Answer

$$y = 9 + 8x^2$ - x^4$

Question 2

Given the function $$f(x) = 9 + 8x^2$ - x^4$, what is f(2$$)$$?

Accepted Answer

$$f(2) = 9 + 8(2^2$) - (2^4$) = 9 + 32 - 16 = 25$$

Question 3

Which of the following best describes the domain of the function $$f(x) = 9 + 8x^2$ - x^4$?

Accepted Answer

All real numbers

Question 4

A function passes the Vertical Line Test if:

Accepted Answer

Every vertical line crosses the graph at most once

Question 5

Given the piecewise function $$f(x) = \begin{cases} x^2$ + 5 & 	ext{if } x \leq 0 \ 3x & 	ext{if } x \u003e 0 \end{cases}$$, what is $$f(-6)$$?

Accepted Answer

$$f(-6) = (-6)^2$ + 5 = 36 + 5 = 41$$

Question 6

For the function $$f(x) = 9 + 8x^2$ - x^4$, which of the following intervals is f(x$$)$$ increasing?

Accepted Answer

On the interval to the left of the relative maximum

Question 7

If $$f(x) = 3x^2$ - 5x + 7$$, what is the simplified form of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$6x + 3h - 5$$

Question 8

Which of the following statements about the range of a function is correct?

Accepted Answer

The range is the set of all possible output (y) values

Question 9

Given the graph of a function with a relative maximum at $$x = 1$$ and a relative minimum at $$x = 3$$, on which interval is the function decreasing?

Accepted Answer

$$1 \u003c x \u003c 3$$

Question 10

Suppose $$f(x) = 9 + 8x^2$ - x^4$. If f(a) = 3$, which of the following equations must a$ satisfy?

Accepted Answer

$$9 + 8a^2$ - a^4$ = 3$$

Question 11

A function is defined as $$f(x) = x^2$ + 5$$ for $$x \leq 0$$ and $$f(x) = 3x$$ for $$x \u003e 0. $$What is the domain of $$f(x)$$?

Accepted Answer

All real numbers

Question 12

Which of the following is NOT a valid function notation?

Accepted Answer

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

Question 13

If a graph contains the point $$(5, -2)$$, what does this tell you about the function $$f$$?

Accepted Answer

$$f(5) = -2$$

Question 14

Which of the following best describes a piecewise function?

Accepted Answer

A function defined by different formulas on different intervals of the domain

Question 15

Given the function $$f(x) = 9 + 8x^2$ - x^4$, what is the y-intercept?

Accepted Answer

$$f(0) = 9$$

Question 16

If $$f(x) = 3x^2$ - 5x + 7$$, what is $$f(x+h)$$?

Accepted Answer

$$3(x+h)^2 - 5(x+h) + 7$

Question 17

Which of the following is a correct interpretation of $$f(3) = 7$$?

Accepted Answer

When the input is $$3$$, the output is $$7$$

Question 18

If a function $$f is $$decreasing on the interval $$(2, 5)$$, which of the following is true?

Accepted Answer

For any $$x_1$$, $$x_2 in$$ $$(2, 5)$$ with $$x_1  f$$($$x_2$$)$$

Question 19

Which of the following is NOT a characteristic of a function?

Accepted Answer

Each output has exactly one input

Question 20

Given the piecewise function $$f(x) = \begin{cases} x^2$ + 5 & 	ext{if } x \leq 0 \ 3x & 	ext{if } x \u003e 0 \end{cases}$$, what is $$f(0)$$?

Accepted Answer

$$f(0) = 0^2$ + 5 = 5$$

Introduction to Functions: Concepts, Notation, and Graphical Analysis

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