FUNCTIONS AND RELATIONS

Unit Overview
This unit is about functions and relations. The graph of a function or relation can often show patterns that data in a chart do not show.

Functions and Relations

Domain and Range (04:59)

Stop! Go to Questions #1-7 about this section, then return to continue on to the next section.

Vertical Line Test

A Practical Example (05:14)

Stop! Go to Questions #8-12 about this section, then return to continue on to the next section.

Function Notation

Try this: Tanya goes to the local grocery store and decides to purchase a salad from the salad bar. The price of the salad is $5.99/lb. Write a function to describe the price of the salad where x is the number of pounds. (Remember that lb. is the abbreviation for pound.)

f (x) = 5.99x

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What is the domain for this function?

x > 0 She cannot buy less than 0 pounds of salad.

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What is the range for this function?

f (x) > 0 Price cannot be less than zero. However, if not much salad is purchased, the price can still be between 0 and 5.99 (if less than one pound of salad is purchased.)

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Try this: Ramon is going on a trip. He fills his fuel tank which holds 14 gallons of fuel. He drives 90 miles and sees that he has 9 gallons of fuel left. Write a function rule that relates the number of miles he can travel to the number
of gallons remaining in the tank.

First: Figure his gas mileage (miles/gallon).

Gas mileage = 18mpg
(driven 90 miles and used 14 – 9 = 5 gallons of gas, 90/5 = 18 miles per gallon)

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Second: How many miles can be driven on a full tank of gas?

14*18= 252miles

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Third: Write the function rule. Consider this: Is amount of gas in the gas tank increasing or decreasing?

f (x) = –18x + 252 f (x) is the output or miles that can be traveled with the remaining fuel. x represents number of gallons of fuel used. As the number of miles traveled increases, the amount of fuel in the car decreases. Hence, why the slope is a negative 18. Each gallon used by the car is 18 miles driven. The y-intercept of 252 represents the number of miles that can be driven on a full tank of gas (14 gallons in the tank × 18 miles per gallon).

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Fourth: What are the domain and range of this problem?

f (x) = –18x + 252 f (x) is the output or miles traveled. Therefore, the range can be as little as 0 miles or as much as 252 (the maximum that can be driven on a tank of gas.) x represents number of gallons of fuel. This can be as little as 0 or as much as can fill the tank, or 14 gallons.
Domain 0 ≤ x ≤ 14,
range 0 ≤ f (x) ≤ 252.

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Function Terminology (12:38)

Stop! Go to Questions #13-32 to complete this unit.

Below are additional educational resources and activities for this unit.

Function Tables

Function Notation