Q: If $$f(x) = 2x + 3$$ and $$g(x) = x^2$ - 1$$, what is $$f(g(2))$$?

$$f(g(2)) = 2 \times (2^2$ - 1) + 3 = 2 \times 3 + 3 = 9$$

Question 1

Which of the following best describes a function?

Accepted Answer

A relation where each x-value is paired with exactly one y-value.

Question 2

Given the relation $$R = \{(2, 5), (3, 7), (2, 8)\}$$, is $$R a $$function? Why or why not?

Accepted Answer

No, because the x-value 2 is paired with two different y-values.

Question 3

What is the domain of the relation $$\{(4, 10), (6, 12), (8, 14)\}$$?

Accepted Answer

$$\{4, 6, 8\}$$

Question 4

Which of the following graphs represents a function?

Accepted Answer

A graph where every vertical line intersects the graph at most once.

Question 5

Let $$f(x) = 2x^2$ - 3x + 1. $$What is $$f(2)$$?

Accepted Answer

Question 6

Let $$f(x) = -x^2$ + 5x - 3. $$Find $$f(2).$$

Accepted Answer

$$3$$

Question 7

Given the function $$g(x) = \sqrt{2x - 1}$$, what is the domain of $$g$$?

Accepted Answer

$$\left[\frac{1}{2}, \infty\right)$$

Question 8

Which of the following is NOT a function?

Accepted Answer

$$y^2 = x$

Question 9

Suppose $$f(x) is $$constant on the interval $$(1, 5). $$What does this mean?

Accepted Answer

For all $$x_1$$, $$x_2 in$$ $$(1, 5)$$, $$f(x_1$) = f(x_2$).$$

Question 10

A swimming pool is being filled with water. The water level increases for 25 hours, stays constant for 25 hours, then decreases for 25 hours, and finally remains constant for 25 hours. Which interval describes when the water level is decreasing?

Accepted Answer

$$(50, 75)$$ hours

Question 11

Given $$f(x) = 3x - 5$$, what is $$f(a + 1)$$?

Accepted Answer

$$3a - 2$$

Question 12

If $$f(x) is $$increasing on $$(a, b)$$, which of the following is true?

Accepted Answer

If $$x_1$$ \u003c $$x_2 in$$ $$(a, b)$$, then $$f(x_1$) \u003c f(x_2$).$$

Question 13

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

Accepted Answer

$$[0, \infty)$$

Question 14

Let $$f(x) = \frac{5}{x-1}. $$What is the domain of $$f$$?

Accepted Answer

$$(-\infty, 1) \cup (1, \infty)$$

Question 15

If $$f(x) = 2x + 3$$ and $$g(x) = x^2$ - 1$$, what is $$f(g(2))$$?

Accepted Answer

$$f(g(2)) = 2 	imes (2^2$ - 1) + 3 = 2 	imes 3 + 3 = 9$$

Question 16

Which of the following statements about function notation is correct?

Accepted Answer

$$f(x)$$ represents the value of the function at x$

Question 17

Given the mapping diagram where $$x-$$values $$\{1, 2, 3\}$$ are each paired with $$y-$$values $$\{4, 5, 6\}$$, and each $$x-$$value is paired with exactly one $$y-$$value, what can you conclude?

Accepted Answer

The relation is a function.

Question 18

A graph passes the vertical line test. What does this indicate?

Accepted Answer

The graph represents a function.

Question 19

Suppose $$y is $$defined by the equation $$y = x + 4. $$What is the range of this function?

Accepted Answer

$$(-\infty, \infty)$$

Relations and Functions: Foundations for Algebraic Graphing and Analysis

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