5.2 Simple Rational Functions

​5.2 Graph Simple Rational Functions

By Sean Brown

Parent Function
f(x) = 1/x

Transformations

How to Graph

Multiple Choice

Identify the horizontal and the vertical asymptotes of the function shown in the graph.

• horizontal asymptote: y = -3; vertical asymptote: x = -4
• horizontal asymptote: x = 3; vertical asymptote: y = -4
• horizontal asymptote: y = -3; vertical asymptote: x = 4
• horizontal asymptote: x = -3; vertical asymptote: y = 4

Multiple Choice

The graph below is a transformation of the parent function f(x) = 1/x. Write the equation of the graph.

• g(x) = 1/(x+3) - 4
• g(x) = 1/(x-) + 4
• g(x) = 1/(x+3) + 4
• g(x) = 1/(x-3) - 4

Multiple Choice

Which of the following represent the graph?

Multiple Choice

What is the horizontal asymptote? 

• x = 2
• x = 7
• y = 2
• y = 7

Multiple Choice

How is this function transformed from the parent function?

• Translated left and up
• Translated right and up
• Translated left and down
• Translated right and down

Multiple Choice

Describe all transformations from the parent function g(x)=1/x to f(x).

• Shift right 5 and shift up 7
• Shift left 7 and shift up 5
• Reflect over the x-axis, shift up 7
• Shift left 5 and shift up 7

Average Cost

in this equation a is the amount of time or number of items being averaged and b is the initial cost.

Example

a gym charges a $20 sign up fee and then $35 per month. Write an equation to find the average cost per month for m months.

Multiple Choice

A sports equipment supplier sells footballs for $4.59 per football and charges $45 in shipping. Write an expression for the average cost per ball of both suppliers.

• $$4.59x+45$$  

• $$45x+4.59$$  

• $$\frac{4.59x+45}{x}$$  

• $$\frac{45x+4.59}{x}$$  

Multiple Choice

From the previous problem, the average cost of a football was $$\frac{4.59x+45}{x}$$  . What would be the average cost of each football if 35 footballs are ordered from the sports store?

• $205.65

• $5.88

• $4.59

• $460.29

Multiple Choice

A softball player has had 13 base hits out of 43 at bats. What is their current batting average?

• 3.308

• .302

• .130

• .430

Multiple Choice

A softball player has had 13 base hits out of 43 at bats. Which expression shows his batting average if he has x more at bats and hits all x of them?

• $$\frac{13}{43}$$  

• $$\frac{13}{43+x}$$  

• $$\frac{13+x}{43}$$  

• $$\frac{13+x}{43+x}$$  

Multiple Choice

Two T-shirt companies sell shirts at different prices. Company A charges a $23 set up fee and $2.29 per shirt. Company B charges $1.99 per shirt and a $35 set up fee. A school club wants to order 20 shirts. Which company has the lowest average cost per shirt?

• Company A with an average cost of $3.44

• Company B with an average cost of $3.74

• Company A with an average cost of $23.11

• Company B with an average cost of $35.10

• Company A with an average cost of $3.22