Question

cp algebra ii final exam review

you need to complete this outside of class. when it is due, you will be given answers so you can check your work after your work has been graded.

topic 1: rational expressions and equations

1. simplify: \\(\frac{x^2-3x-10}{x^2+7x+10}\\)

1. multiply: \\(\frac{3x-9}{x^2-4} \cdot \frac{x^2-4x+4}{x^2+3x+2}\\)

1. divide: \\(\frac{x^2-2x-8}{x+3} \div \frac{x-4}{x+3}\\)

1. solve each equation:

a. \\(\frac{x+3}{x-1} = 5\\)
b. \\(\frac{2x+3}{x-1} = 4\\)
c. \\(\frac{5x-3}{2x+3} = 3\\)

topic 2: rational graphs

1. find the vertical asymptotes and holes:

a. \\(f(x) = \frac{(x+2)(x+4)(x+1)}{(x-4)(x+2)}\\)
b. \\(f(x) = \frac{x^2-6x+8}{x^2-4}\\)
c. \\(f(x) = \frac{x-3}{x^2-x-12}\\)

1. find the vertical and horizontal asymptotes:

a. \\(f(x) = \frac{1}{x+2} + 3\\)
b. \\(f(x) = \frac{1}{x-2} - 3\\)
c. \\(f(x) = \frac{1}{x-4} + 2\\)

1. write a rational function that has a vertical asymptote at \\(x = 7\\) and a hole at \\(x = -4\\).

Explanation:

Simplify, multiply, and divide rational expressions

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Solve rational equations

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Find vertical asymptotes, holes, and horizontal asymptotes

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Answer:

Topic 1: Rational Expressions and Equations

Question 1

$$\frac{x-5}{x+5}$$

Question 2

$$\frac{3(x-3)(x-2)}{(x+2)^2(x+1)}$$

Question 3

$$x+2$$

Question 4

a.

$$x = 2$$

b.

$$x = \frac{7}{2}$$

c.

$$x = -12$$

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Topic 2: Rational Graphs

Question 5

a. Vertical Asymptote: \(x = 4\); Hole: \(x = -2\)
b. Vertical Asymptote: \(x = -2\); Hole: \(x = 2\)
c. Vertical Asymptotes: \(x = 4, x = -3\); Holes: None

Question 6

a. Vertical Asymptote: \(x = -2\); Horizontal Asymptote: \(y = 3\)
b. Vertical Asymptote: \(x = 2\); Horizontal Asymptote: \(y = -3\)
c. Vertical Asymptote: \(x = 4\); Horizontal Asymptote: \(y = 2\)

Question 7

$$f(x) = \frac{x+4}{(x-7)(x+4)}$$