Graphs of Rational Functions

1. There are many cylinders with a volume of 144 $\pi$   cubic inches. The height h(r) in inches of one of these cylinders is a function of its radius in inches where  $h\left(r\right)=\frac{144}{r^2}$  . What is the height of one of these cylinders if its radius is 2 inches?

• 72 inches

• 36 inches

• 144 inches

• not enough information

The surface area S(r) in square units of a cylinder with a volume of 20 cubic units is a function of its radius r in units where  $S\left(r\right)=2\pi r^2+\frac{40}{r}$  . What is the surface area of a cylinder with a volume of 20 cubic units and a radius of 4 units?

• 110.5 sq. in.

• 35.1 sq. in.

• 100.5 sq. in.

• not enough information

Tags

CCSS.HSA.SSE.A.1

CCSS.HSG.GMD.A.3

What is the vertical asymptote for $f\left(x\right)=\frac{7}{x-1}$  ?

• x=0

• x=7

• x=-1

• x=1

Which function matches this graph?

• $f\left(x\right)=\frac{4}{x-2}$

• $f\left(x\right)=\frac{4}{x+2}$

• $f\left(x\right)=\frac{-4}{x-2}$

• $f\left(x\right)=\frac{-4}{x+2}$

Tags

CCSS.HSF-IF.C.7D

Which function matches this graph?

• $f\left(x\right)=\frac{4}{x}+1$

• $f\left(x\right)=\frac{4}{x}-1$

• $f\left(x\right)=\frac{4}{x-1}$

• $f\left(x\right)=\frac{4}{x+1}$

Tags

CCSS.HSF-IF.C.7D

Which functions match this graph?

• $f\left(x\right)=\frac{4}{x}+1$

• $f\left(x\right)=\frac{4}{x}-1$

•  $f\left(x\right)=\frac{x+4}{x}$ 

•  $f\left(x\right)=\frac{4-x}{x}$ 

What is the end behavior of $f\left(x\right)=\frac{5x+2}{x-3}$  ?

• The graph approaches y=2.

• The graph approaches y=5x+2.
  

• The graph approaches y=3.

• The graph approaches y=0.

What is the end behavior of $f\left(x\right)=\frac{99+9x}{x}$  as x gets larger and larger?

• The value of the expression gets closer and closer to 0.

• The value of the expression gets closer and closer to 1.

• The value of the expression gets closer and closer to 9.

• The value of the expression gets closer and closer to 99.

Tags

CCSS.HSF-IF.C.7D

Which function matches this graph?

• $f\left(x\right)=\frac{1}{x-1}+2$

• $f\left(x\right)=\frac{1}{x+2}-1$

• $f\left(x\right)=\frac{1}{x+1}+2$

• $f\left(x\right)=\frac{1}{x-2}+1$

Tags

CCSS.HSF-IF.C.7D

Rewrite the rational function $f\left(x\right)=\frac{x^2+5x-17}{x-3}$  in the form  $f\left(x\right)=p\left(x\right)+\frac{r}{x-3}$  

•  $f\left(x\right)=x+8+-\frac{24}{x-3}$  

•  $f\left(x\right)=x+2\ +-\frac{23}{x-3}$  

•  $f\left(x\right)=x+8+\frac{7}{x-3}$  

•  $f\left(x\right)=x+8+-\frac{7}{x-3}$