Q: A scientist records the average high temperature in Los Angeles for the first five months of the year as follows: January: $$68^\circ F$$, February: $$69^\circ F$$, March: $$70^\circ F$$, April: $$73^\circ F$$, May: $$74^\circ F. $$Which of the following best represents the domain of this relation?

$$\{\text{January}, \text{February}, \text{March}, \text{April}, \text{May}\}$$

Question 1

Which of the following best describes a function?

Accepted Answer

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

Question 2

Given the function $$f(x) = x^2$ - 2x$$, what is $$f(3)$$?

Accepted Answer

$$3$$

Question 3

Which of the following sets of ordered pairs represents a function?

Accepted Answer

$$\{(1,2), (2,3), (3,4)\}$$

Question 4

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

Accepted Answer

$$-11$$

Question 5

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

Accepted Answer

$$y = 3x + 2$$

Question 6

Given $$f(x) = x^2$ - 2x$$, what is $$f(x+h) in $$terms of $$x$$ and $$h$$?

Accepted Answer

$$x^2 + 2xh$$ + $$h^2 - 2x - 2h$

Question 7

The difference quotient for a function $$f(x) is $$given by $$\frac{f(x+h) - f(x)}{h}. $$For $$f(x) = 3x$$, what is the difference quotient?

Accepted Answer

$$3$$

Question 8

What is the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 9

A scientist records the average high temperature in Los Angeles for the first five months of the year as follows: January: $$68^\circ F$$, February: $$69^\circ F$$, March: $$70^\circ F$$, April: $$73^\circ F$$, May: $$74^\circ F. $$Which of the following best represents the domain of this relation?

Accepted Answer

$$\{	ext{January}, 	ext{February}, 	ext{March}, 	ext{April}, 	ext{May}\}$$

Question 10

Which of the following graphs passes the vertical line test and therefore represents a function?

Accepted Answer

A parabola opening upwards

Question 11

Given $$f(x) = \frac{1}{x-3}$$ and $$g(x) = \frac{x}{x-2}$$, what is the domain of $$f(x) + g(x)$$?

Accepted Answer

$$(-\infty, 2) \cup (2, 3) \cup (3, \infty)$$

Question 12

If $$f(x) = x^2$ - 2x$$, what is $$f(-x)$$?

Accepted Answer

$$x^2 + 2x$

Question 13

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

Accepted Answer

As a single number

Question 14

Given $$f(x) = x^2$ - 2x$$, what is $$f(x+2)$$?

Accepted Answer

$$(x+2)^2 - 2(x+2$$) = $$x^2 + 4x + 4 - 2x - 4$$ = $$x^2 + 2x$

Question 15

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

Accepted Answer

$$[2, \infty)$$

Question 16

Suppose $$f(x) = x^2$ and g(x) = x+1$. What is (f-g)(x$$)$$?

Accepted Answer

$$x^2 - x - 1$

Question 17

A function $$f is $$defined by $$f(x) = \frac{1}{x^2$ - 9}. $$What is the domain of $$f$$?

Accepted Answer

$$(-\infty, -3) \cup (-3, 3) \cup (3, \infty)$$

Question 18

Which of the following statements about the vertical line test is true?

Accepted Answer

A graph represents a function if and only if every vertical line intersects the graph at most once.

Question 19

If $$f(x) = x^2$ - 2x$$, what is $$f(2x)$$?

Accepted Answer

$$4x^2 - 4x$

Question 20

Given $$f(x) = x^2$ - 2x$$, what is $$f(x) + f(-x)$$?

Accepted Answer

$$2x^2$$

College Algebra Study Notes: Functions and Their Properties

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