Rational Functions and End Behavior

Lesson 17 Graphs of Rational Functions Part 1

Multiple Choice

Jada is planning a kayak trip. She finds an expression for the time, T(s), in hours it takes her to paddle 10 kilometers upstream in terms of s, the speed of the current in kilometers per hour. This is the graph Jada gets if she allows s to take on any value between 0 and 7.5.

What would be a more appropriate domain for Jada to use instead?

• $$0<x<5$$

• $$0<x<4.5$$

• $$0<x<6$$

• $$all\ real\ numbers$$

Multiple Choice

Jada is planning a kayak trip. She finds an expression for the time, T(s), in hours it takes her to paddle 10 kilometers upstream in terms of s, the speed of the current in kilometers per hour. This is the graph Jada gets if she allows s to take on any value between 0 and 7.5.

What is the approximate speed of the current if her trip takes 6 hours?

• About 3.8 km per hour

• About 10 km per hour
  

• About -3.8 km per hour
  

• About0 km per hour
  

Open Ended

A cylindrical can needs to have a volume of 6 cubic inches. A label is to go around the side of the can. The function S(r)=12/r gives the area of the label in square inches where r is the radius of the can in inches.

As r gets closer and closer to 0, what does the behavior of the function tell you about the situation?

As r gets larger and larger, what does the end behavior of the function tell you about the situation?

Open Ended

Feedback from the last question.

a. As the radius gets smaller the surface area gets larger.

b. As the radius gets larger the surface area gets smaller.

Multiple Choice

What is the equation of the vertical asymptote for the graph of the rational function?

$$g\left(x\right)=\frac{6}{x-1}$$  

• x=1

• x=-1

• x=6

• x=1/6

Open Ended

A geometric sequence h starts at 16 and has a growth factor of 1.75. Sketch a graph of h showing the first 5 terms.

Multiple Choice

Choose the equation of the graph shown.

• $$g\left(x\right)=-x^2\left(x-2\right)$$

• $$h\left(x\right)=x^2\left(x-2\right)$$

Open Ended

Technology required. A 6 oz cylindrical can of tomato paste needs to have a volume of 178 cm3. The current can design uses a radius of 2.75 cm and a height of 7.5 cm. Use graphing technology to find a cylindrical design that would have less surface area so each can uses less metal.

Multiple Select

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?
Choose all that apply.

• $$32\pi+10$$  

• $$32\pi$$  

• 110.53

• 100.532