Chapter 11: Rational Functions and Equations

Identify the asymptotes of the function.

$\mathit{y}\mathbf{=}\frac{\mathbf{3}}{\mathbf{2}\mathbf{x}\mathbf{+}\mathbf{4}}$

Peggy is having a cement walkway installed around the perimeter of her swimming pool with the dimensions shown below. If$x=3$ find the area, in square feet, of the pool and walkway.

Simplify each expression. State the excluded values of the variables.

$\frac{4x-28}{x^2-49}$

Find the GCF of each pair of monomials.

$\mathbf{60}{\mathit{r}}^2\mathbf{,}\mathbf{45}{\mathit{r}}^3$

Solve. Assume that $y$varies inversely as $x$.

If$y=8$when$x=4$finding $x$when $y=2$.

Identify the asymptotes of the function.

$\mathit{y}\mathbf{=}\frac{\mathbf{2}}{\mathbf{x}\mathbf{-}\mathbf{4}}$

Find the GCF of each pair of monomials.

$12xy,16x^{2}y$

MULTIPLE CHOICE The area of a rectangle is $x^2+5x+6$square feet. If the width is $x+2$, what is the length of the rectangle.

1. $x+2$
   
2. $x+3$
   
3. 1
4. 3

Use the equation $y=2\left(4+x\right)$to answer each question.

a. Complete the following table for the different values of $x$.

b. Plot the points from the table on a coordinate grid. What do you notice about the points?

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.

A direct variation can be represented by an equation of the form$k=xy$, where k is a nonzero constant.