1.3 Independent and Dependent Variables

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The input of a function is the independent variable. The output of a function is the dependent variable. The value of the dependent variable depends on, or is a function of, the value of the independent variable.

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Example 2A: Identifying Independent and Dependent Variables

Identify the independent and dependent variablesin the situation.

A painter must measure a room before deciding how much paint to buy.

The amount of paint depends on the measurement of a room.

Dependent: amount of paintIndependent: measurement of the room

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Identify the independent and dependent variablesin the situation.

The height of a candle decrease d centimeters for every hour it burns.

Dependent: height of candle Independent: time

The height of a candle depends on the number of hours it burns.

Example 2B: Identifying Independent and Dependent Variables

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A veterinarian must weight an animal before determining the amount of medication.

The amount of medication depends on the weight of an animal.

Dependent: amount of medicationIndependent: weight of animal

Identify the independent and dependent variablesin the situation.

Example 2C: Identifying Independent and Dependent Variables

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Helpful Hint

There are several different ways to describe the variables of a function.

IndependentVariable

DependentVariable

x-values y-values

Domain Range

Input Output

x f(x)

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Check It Out! Example 2a

A company charges $10 per hour to rent a jackhammer.

Identify the independent and dependent variable in the situation.

The cost to rent a jackhammer depends on the length of time it is rented.

Dependent variable: costIndependent variable: time

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Identify the independent and dependent variable in the situation.

Check It Out! Example 2b

Camryn buys p pounds of apples at $0.99 per pound.

The cost of apples depends on the number of pounds bought.

Dependent variable: costIndependent variable: pounds