Q: Suppose the function $$f(x) = x^2$ - 4x + 7. $$What is $$f(3)$$?

$$f(3) = 3^2$ - 4 \times 3 + 7 = 9 - 12 + 7 = 4$$

Q: A scientist records the average high temperature in Los Angeles for the first five months of the year as shown in the table. What is the domain of this relation?

The set of months: $$\{\text{January}, \text{February}, \text{March}, \text{April}, \text{May}\}$$

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

$$(f+g)(3) = f(3) + g(3) = (2 \times 3 + 1) + (3^2$) = 7 + 9 = 16$$

Question 1

Which of the following best describes the difference between a relation and a function?

Accepted Answer

A function pairs each element of the domain with exactly one element of the range, while a relation can pair an element of the domain with multiple elements of the range.

Question 2

Given the set of ordered pairs $$\{(1, 6), (3, 9), (6, 1), (9, 2)\}$$, which of the following is true?

Accepted Answer

This set represents a function because each input has exactly one output.

Question 3

Consider the mapping diagram where each person is paired with their birthday. If two people share the same birthday, does this mapping represent a function from people to birthdays?

Accepted Answer

Yes, because each person is assigned exactly one birthday.

Question 4

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

Accepted Answer

A single number

Question 5

Suppose the function $$f(x) = x^2$ - 4x + 7. $$What is $$f(3)$$?

Accepted Answer

$$f(3) = 3^2$ - 4 	imes 3 + 7 = 9 - 12 + 7 = 4$$

Question 6

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

Accepted Answer

$$[2, \infty)$$

Question 7

If $$g(x) = \dfrac{1}{x-5}$$, for which value of $$x is$$ $$g(x)$$ undefined?

Accepted Answer

$$x = 5$$

Question 8

A scientist records the average high temperature in Los Angeles for the first five months of the year as shown in the table. What is the domain of this relation?

Accepted Answer

The set of months: $$\{	ext{January}, 	ext{February}, 	ext{March}, 	ext{April}, 	ext{May}\}$$

Question 9

Which of the following equations defines $$y as a $$function of $$x$$?

Accepted Answer

$$y = 2x + 5$$

Question 10

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

Accepted Answer

$$(f+g)(3) = f(3) + g(3) = (2 	imes 3 + 1) + (3^2$) = 7 + 9 = 16$$

Question 11

Which of the following best describes the range of a function?

Accepted Answer

The set of all possible output values

Question 12

Given $$f(x) = x^2$ and g(x) = x + 1$, what is the domain of the quotient function $$\dfrac{f}{g}$$?

Accepted Answer

All real numbers except $$x = -1$$

Question 13

If $$f(x) = x^2$ - 4$$ and $$h(x) = \sqrt{x}$$, what is the domain of $$(f+h)(x)$$?

Accepted Answer

All real numbers $$x \geq 0$$

Question 14

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

Accepted Answer

Assigning each student in a class to their unique student ID number

Question 15

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

Accepted Answer

$$\dfrac{f(x+h) - f(x)}{h} = \dfrac{(x+h)^2$ - x^2$}{h} = \dfrac{2xh + h^2$}{h} = 2x + h$$

Question 16

If the area $$A of a $$right triangle is given as a function of the shorter leg $$x$$, and the other leg is triple the shorter leg, which function represents the area?

Accepted Answer

$$A(x) = \dfrac{1}{2} x (3x) = \dfrac{3}{2} x^2$

Question 17

Which of the following best describes the independent variable in a function?

Accepted Answer

The variable that can be freely chosen from the domain

Question 18

Given $$f(x) = x^2$ and g(x) = x - 2$, what is the domain of the product function f$$ \cdot g$$?

Accepted Answer

All real numbers

Functions and Their Graphs: Foundations and Representations

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