Question 1

Which of the following equations represents a vertical line passing through $$x = -3$$?

Accepted Answer

$$x = -3$$

Question 2

Given the points $$A(2, 5)$$ and $$B(6, 1)$$, what is the distance between them?

Accepted Answer

$$\sqrt{(6-2)^2$ + (1-5)^2$} = \sqrt{16 + 16} = \sqrt{32}$$

Question 3

Which of the following is the correct midpoint of the segment joining $$P_1(5$$, 5)$$ and P_2$(-3, 1)$$?

Accepted Answer

$$(1, 3)$$

Question 4

A function $$f is $$defined as $$f(x) = 2x^2$ - 3x. $$What is the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$4xh + 2h^2$ - 3h$$

Question 5

Which of the following relations is NOT a function?

Accepted Answer

$$\{(1,4), (2,4), (0,0), (1,8)\}$$

Question 6

Given the equation $$y = x^2$ - 4$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 2, -2$$

Question 7

Which of the following best describes the symmetry of the equation $$y^2$$ = $$x^2$$?

Accepted Answer

Symmetric with respect to both axes and the origin

Question 8

If $$f(x) = 2x - 5$$, what is $$f(-1)$$?

Accepted Answer

$$-7$$

Question 9

Which of the following is the correct domain for the function $$f(x) = \sqrt{x+2}$$?

Accepted Answer

$$x \geq -2$$

Question 10

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

Accepted Answer

$$3x^2 + 3x - 3$

Question 11

Which of the following best describes an odd function?

Accepted Answer

A function whose graph is symmetric with respect to the origin

Question 12

For the line passing through $$(3,2)$$ with slope $$m = 4$$, what is the equation in point-slope form?

Accepted Answer

$$y - 2 = 4(x - 3)$$

Question 13

Which of the following intervals describes where the function in the graph is increasing?

Accepted Answer

$$[-4, 0)$$

Question 14

If $$f(x) = 2x^2$ - x - 1$$, what is $$f(-1)$$?

Accepted Answer

$$2$$

Question 15

Which of the following is the correct slope-intercept form for a line with slope $$m = 2$$ and passing through $$(3, 3)$$?

Accepted Answer

$$y = 2x - 3$$

Question 16

Given $$f(x) = 2x + 3$$ and $$g(x) = 4x - 4$$, what is $$(f \cdot g)(x)$$?

Accepted Answer

$$8x^2 + 4x - 12$

Question 17

Which of the following is the correct definition of the range of a relation?

Accepted Answer

The set of all possible $$y-$$values

Question 18

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

Accepted Answer

$$2x^2 - 4x + 1$

Question 19

Which of the following is the correct formula for the distance between two points $$P_1$$($$x_1$$, $$y_1$$)$$ and P_2$(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

College Algebra Study Notes: Equations, Graphs, and Functions

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