Key Concepts:

Learning the characteristics of functions

SAT PROBLEM:

Define f(x)=100−x2−−−−−−−√3

Give the domain of f.

Possible Answers:

[0,10]

\left [-10, \infty)

[−10,10]

(−∞,10]

(−∞,∞)

Correct Answer: (−∞,∞)

REAL WORLD APPLICATION:

Let's start with an example. Suppose the gas tank in Zack's car holds 20 gallons of gas, and the car gets 32 miles per gallon. Zack fills up his tank with gas and heads out on a trip. His distance (or D) traveled on one tank of gas can be represented by the function:

• Mathematically speaking, the number of gallons Zack can possibly use would be the domain of the function, and the possible number of miles traveled would be the range of the function. The domain consists of the values that can be put into a function that make sense (that is, values that don't make the function undefined). In other words, Zack can put up to 20 gallons into his tank: It wouldn't make sense to put 21 gallons in because one would spill out. The range of a function is the set of values that come out of a function based on the function's domain.
• Let's take a look at our function D(x) = 32x and put this into context. As we said, the domain is the possible number of gallons of gas used. This is represented by x in the function, or the input value. Makes sense, doesn't it? The input values are the domain of the function, so the number of gallons used is the domain. Similarly, the output values, or D(x), represent the range, so the range is the possible distance traveled.