Question 1

Which of the following best describes a rational equation?

Accepted Answer

An equation that contains a variable in the denominator.

Question 2

Given the equation $$y = -2x^2$ + 4$$, what is the y-intercept of the graph?

Accepted Answer

$$(0, 4)$$

Question 3

If the window settings for a graphing calculator are changed from $$x$$ minimum $$= -10$$, $$x$$ maximum $$= 10$$, $$y$$ minimum $$= -10$$, $$y$$ maximum $$= 10 to$$ $$x$$ minimum $$= -4$$, $$x$$ maximum $$= 4$$, $$y$$ minimum $$= -6$$, $$y$$ maximum $$= 6$$, what effect does this have on the graph of $$y = x^2$ - 6$$?

Accepted Answer

The graph will appear more compressed horizontally and vertically.

Question 4

Solve the equation $$8x - 5x - 2 = 5x - 10$$ for $$x.$$

Accepted Answer

$$x = -2$$

Question 5

Which of the following is an extraneous solution to the equation $$\frac{x}{x+1} = \frac{7}{x+1}$$?

Accepted Answer

$$x = -1$$

Question 6

What is the least common denominator (LCD) for the rational equation $$\frac{1}{x-3} + \frac{1}{x+2} = 0$$?

Accepted Answer

$$(x-3)(x+2)$$

Question 7

Given the equation $$y = x^2$ + 5x + 4$$, which of the following points lies on the graph?

Accepted Answer

$$(0, 4)$$

Question 8

Solve for $$x in $$the equation $$x + 2x^2$ = 5x + 2$$ algebraically.

Accepted Answer

$$x = \frac{2}{5}$$

Question 9

Which of the following is a restriction for the rational equation $$\frac{1}{x-6} = 2$$?

Accepted Answer

$$x 
eq 6$$

Question 10

If a point $$(a, b) is on $$the graph of $$y = 2x^2$ + 3x - 5$$, which equation must be true?

Accepted Answer

$$b = 2a^2$ + 3a - 5$$

Question 11

Which of the following best describes the $$x-$$intercept of a graph?

Accepted Answer

The point where $$y = 0.$$

Question 12

Solve for $$t in $$the formula $$A = P + Prt.$$

Accepted Answer

$$t = \frac{A-P}{Pr}$$

Question 13

Which of the following is NOT a step in solving rational equations algebraically?

Accepted Answer

Graph the equation and estimate the solution.

Question 14

Given the equation $$y = x^2$ - 6$$, what is the $$y-$$value when $$x = -2$$?

Accepted Answer

$$y = -2$$

Question 15

Which of the following is an example of an extraneous solution?

Accepted Answer

A solution that makes the denominator zero in the original equation.

Question 16

If the $$x-$$intercepts of a graph are $$(-3, 0)$$ and $$(4.5, 0)$$, what are the solutions to the equation represented by the graph?

Accepted Answer

$$x = -3$$ and $$x = 4.5$$

Question 17

Which of the following window settings would best display the vertex of $$y = x^2$ - 6$$?

Accepted Answer

$$x$$ minimum $$= -4$$, $$x$$ maximum $$= 4$$, $$y$$ minimum $$= -6$$, $$y$$ maximum $$= 6$$

Question 18

Solve the equation $$\frac{1}{x-6} = 2$$ for $$x.$$

Accepted Answer

$$x = 8$$

Question 19

Which of the following is the correct solution to $$x + 2x^2$ = 5x + 2$$?

Accepted Answer

$$x = \frac{2}{5}$$

Precalculus Study Notes: Graphing Equations, Linear and Rational Equations

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