Question 1

Which of the following is the correct simplification of the rational expression $$\frac{(x+5)(x-1)}{(x+3)(x-1)}$$?

Accepted Answer

$$\frac{x+5}{x+3}$$

Question 2

Solve for $$x in $$the equation $$3x - 2 = 7x + 4.$$

Accepted Answer

$$x = -1$$

Question 3

Given the equation $$x^2 + 4x + 2x = 12$, what are the solutions for x$?

Accepted Answer

$$x = -6, x = 2$$

Question 4

Which of the following is the correct factorization of $$x^2 + 4x - 12$?

Accepted Answer

$$(x+6)(x-2)$$

Question 5

If $$f(x) = \frac{x^2$}{(x-3)(x-2)}$$, what is the $$y-$$intercept of the graph of $$f(x)$$?

Accepted Answer

$$(0, 0)$$

Question 6

For the function $$f(x) = \frac{x^2$}{(x-3)(x-2)}$$, which of the following is a vertical asymptote?

Accepted Answer

$$x = 2$$ and $$x = 3$$

Question 7

Given $$f(x) = \frac{x-3}{x-2}$$, what is the $$x-$$intercept of the graph?

Accepted Answer

$$(3, 0)$$

Question 8

Which of the following describes the horizontal asymptote of $$f(x) = \frac{x^2$}{(x-3)(x-2)}$$?

Accepted Answer

There is no horizontal asymptote

Question 9

A medical dosage formula is given by $$D(x) = \frac{5}{(x-1)(x+1)}$$, where $$x is $$the number of hours since administration. What is the value of $$D(2)$$?

Accepted Answer

$$\frac{5}{3}$$

Question 10

Solve for $$x in $$the equation $$2x + x^2$ - x = 3.$$

Accepted Answer

$$x = 1, x = -3$$

Question 11

Which of the following is the correct simplification of $$\frac{(x+1)(x-1)}{(x^2$-1)}$$?

Accepted Answer

$$1$$

Question 12

A chemical reaction rate is modeled by $$R(x) = \frac{x-1}{(x-3)^2$}$$, where $$x is $$the concentration. What happens to $$R(x) as$$ $$x$$ approaches $$3$$?

Accepted Answer

$$R(x)$$ approaches $$\infty$$

Question 13

Given $$f(x) = \frac{x^2$-1}{x^2$-4}$$, which of the following is a hole in the graph?

Accepted Answer

There is no hole

Question 14

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

Accepted Answer

All real numbers except $$x = 1$$ and $$x = -1$$

Question 15

A population model is given by $$P(x) = \frac{x^2$+4x+4}{x+2}. $$What is the simplified form of $$P(x)$$?

Accepted Answer

$$x+2$$

Question 16

Which of the following is the correct solution to $$x^2 - 5x + 6 = 0$?

Accepted Answer

$$x = 2, x = 3$$

Question 17

If $$f(x) = \frac{x^2$-9}{x^2$-4}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 2$$ and $$x = -2$$

Question 18

A rational function $$f(x) = \frac{x-1}{x^2$-1} is $$used to model the rate of a reaction. What is the $$y-$$intercept?

Accepted Answer

$$(0, -1)$$

Question 19

Which of the following is the correct solution to $$2x^2 + 3x - 2 = 0$?

Accepted Answer

$$x = -2, x = \frac{1}{2}$$

Solving Rational Equations and Analyzing Rational Functions

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