Rational Functions - Review

1.    Which response represents the solution to the rational equation below?

    $\frac{1}{x-4}+\frac{6}{x}=\frac{3}{x}$  

•  $x=0,\ x=4$  

•  $x=3$  

•  $x=0,\ x=3$  

•  $x=4$  

The amount of time needed to stuff and address envelopes for the local high school’s fundraising campaign varies inversely with the number of student and parent volunteers that attend the envelope stuffing event. Last year, it took 20 people 3 hours to stuff and address the envelopes.

Select the equation that could be used to estimate the amount of time, y, it will take x number of volunteers to stuff and address the same number of envelopes.

• 
  

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

• $y=60x$

• $y=\frac{60}{x}$

• $y=7x$

The amount of time needed to stuff and address envelopes for the local high school’s fundraising campaign varies inversely with the number of student and parent volunteers that attend the envelope stuffing event. Last year, it took 20 people 3 hours to stuff and address the envelopes.

How many volunteers are needed to stuff and address all the envelopes in 2 hours?

• 10 volunteers

• 30 volunteers

• 20 volunteers

• 40 volunteers

Multiply the rational expression below and record any excluded values. 

 $\frac{x^2+7x+6}{x^2+x-2}\cdot\frac{x^2-x-6}{x^2+3x-18}$  

•  $1,x≠-6,-2,1,3$  

•  $\frac{x(x+1)}{(x-1)(x+2)}\ ,x≠-6,-2,1,3$  

•  $\frac{(x+1)(x+7)}{(x-1)(x-6)},x≠1,2,3,6$  

•  $\frac{X+1}{X-1},x≠-6,-2,1,3$  

What is the vertical asymptote of the function below?

 $f\left(x\right)=\frac{x^2-2x-8}{x^2+2x-24}$  

•  $y=1$  

•  $x=4$  

•  $x=-2$  

•  $x=-6$  

Which response represents the solution to the rational equation below?

 $\frac{5}{x+8}=\frac{2}{x-1}$  

•  $x=7$  

•  $x=3$  

•  $x=-8$  

•  $x=0$  

A young entrepreneur purchased a custom-painted lemonade stand for $30. Each cup of lemonade sold costs $0.25 in materials. Let x=number of lemonade cups sold. Which function represents the average cost, c, of a cup of lemonade?

• $c(x)=\frac{30+0.25x}{x}$

• $c(x)=\frac{30}{x}$

• $c(x)=30+0.25x$

• $c(x)=0.25x$

The equation for g(x) was obtained by transforming   $f\left(x\right)=\frac{1}{x}$  . Which description best describes the transformations performed on f(x) to obtain g(x)?

 $g\left(x\right)=\frac{2}{x+16}$  

• Vertical stretch by a factor of  $\frac{1}{2}$  followed by a horizontal translation right 16 units.

• Vertical stretch by a factor of  $\frac{1}{2}$  followed by a vertical translation up 16 units.

• Vertical stretch by a factor of 2 followed by a horizontal translation left 16 units.

• Vertical stretch by a factor of 2 followed by a vertical translation down 16 units.

The function g(x) was obtained by transforming   $f\left(x\right)=\frac{1}{x}.$  The function  $f\left(x\right)$  is reflected about the x-axis then translated up 12 units. Which equation represents  $g\left(x\right)?$  

•  $g\left(x\right)=\frac{1}{x-12}$  

•  $g\left(x\right)=-\frac{1}{x+12}$  

•  $g\left(x\right)=-\frac{1}{x}+12$  

•  $g\left(x\right)=\frac{1}{x}-12$  

The graph of a function passes through the point (3, 8). If y varies inversely as x, write a function relating x and y.

• 
  

  $y=\frac{24}{x}$
  

• $y=11x$

• $y=\frac{11}{x}$

• $y=24x$