Chapter 11: Rational Functions and Equations

Solve each proportion.

$\frac{5}{12}\mathbf{=}\frac{\mathbf{x}}{36}$

Find the distance between$\left(3,-6\right)$ and$\left(1,4\right)$ on a coordinate grid. Round to the nearest tenth.

1. $8.1$
2. $8.5$
3. $9.6$
4. $10.2$

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

If the line $x=a$ is a vertical asymptote of a rational function, then a is an excluded value.

Assume that$\mathit{y}$ varies inversely as $\mathit{x}$. Write an inverse variation equation that relates$\mathit{x}$ and $\mathit{y}$.

$\mathit{y}\mathbf{=}\mathbf{-}\mathbf{2}$when $\mathit{x}\mathbf{=}\mathbf{12}$.

Determine whether each table or equation represents an inverse or a direct variation. Explain.

$\mathit{x}\mathit{y}\mathbf{=}\mathbf{4}$

Find each product or quotient.

$\frac{\left(x+6\right)\left(x-2\right)}{x^3}\cdot \frac{7x^2}{x-3}$

If $y$varies inversely as $x$and $y=4$when$x=-8$find $y$when$x=-4$.

Find each product or quotient.

$\frac{x^2}{x+4}÷\frac{3x}{x^2-16}$

Find each product or quotient.

$\frac{3b-12}{b+4}÷\left(b^2-6b+8\right)$

Find each product or quotient.

$\frac{2a^2+7a-15}{a+5}÷\frac{9a^2-4}{3a+2}$