# Lesson 17

Graphs of Rational Functions (Part 1)

### Problem 1

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.

1. What would be a more appropriate domain for Jada to use instead?
2. What is the approximate speed of the current if her trip takes 6 hours?

### Problem 2

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 $$S(r)=\frac{12}{r}$$ gives the area of the label in square inches where $$r$$ is the radius of the can in inches.

1. As $$r$$ gets closer and closer to 0, what does the behavior of the function tell you about the situation?
2. As $$r$$ gets larger and larger, what does the end behavior of the function tell you about the situation?

### Problem 3

What is the equation of the vertical asymptote for the graph of the rational function $$g(x) = \frac{6}{x-1}$$?

A:

$$x=1$$

B:

$$x=\text-1$$

C:

$$x=6$$

D:

$$x=\frac{1}{6}$$

### Problem 4

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.

### Solution

(From Unit 1, Lesson 7.)

### Problem 5

Is this the graph of $$g(x)=\text-x^2(x-2)$$ or $$h(x)=x^2(x-2)$$? Explain how you know.

### Solution

(From Unit 2, Lesson 10.)

### Problem 6

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.

### Solution

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