$$\{x \mid x \neq 2, x \neq -2\}$$

Question 1

Which of the following relations is a function?

Accepted Answer

The set of ordered pairs $$\{(2,5), (3,6), (4,7)\}$$

Question 2

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

Accepted Answer

$$\{x \mid x 
eq 3\}$$

Question 3

For the function $$f(x) = x^2$ - 4x + 3$$, on which interval is the function decreasing?

Accepted Answer

$$(-\infty, 2)$$

Question 4

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 5

Calculate the slope of the line passing through the points $$(2, 5)$$ and $$(6, 13).$$

Accepted Answer

$$2$$

Question 6

What is the equation of the line in point-slope form passing through $$(1, -2)$$ with slope $$m = 3$$?

Accepted Answer

$$y + 2 = 3(x - 1)$$

Question 7

Which of the following lines is perpendicular to $$y = 2x + 5$$?

Accepted Answer

$$y = -\frac{1}{2}x + 3$$

Question 8

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

Accepted Answer

$$(x + 1)^2$

Question 9

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

Accepted Answer

$$\{x \mid x \geq 2\}$$

Question 10

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, write h(x) = f(g(x$$))$$ as a composition.

Accepted Answer

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

Question 11

Which pair of functions are inverses of each other?

Accepted Answer

$$f(x) = 2x + 3$$ and $$g(x) = \frac{x - 3}{2}$$

Question 12

Find the inverse of the function $$f(x) = 5x - 7.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{x + 7}{5}$$

Question 13

What is the distance between the points $$(3, 4)$$ and $$(7, 1)$$?

Accepted Answer

$$5$$

Question 14

A function $$f(x) is $$even if:

Accepted Answer

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

Question 15

Which transformation represents a vertical shift up by 3 units for $$f(x)$$?

Accepted Answer

$$f(x) + 3$$

Question 16

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

Accepted Answer

$$4x^2$$

Question 17

Which of the following equations represents a function?

Accepted Answer

$$y = x^3$ + 2$$

Question 18

Given the function $$f(x) = \frac{1}{x^2$ - 4}$$, what is its domain?

Accepted Answer

$$\{x \mid x 
eq 2, x 
eq -2\}$$

Question 19

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is f(g(x$$))$$?

Accepted Answer

$$x$$

College Algebra Exam Question Topics – Step-by-Step Study Guidance

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