3.3 Modeling with Functions

3.3 Modeling with Functions

Essential Question: What is function notation and how can you use functions to model real-world situations?

​Vocabulary

​​A relation is a set of ordered pairs (x,y) where x is the input value and y is the output value.

​The domain is all possible inputs of a relation, and the range is all possible outputs of a relation.

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​The input of function is the independent variable.

​The output of the 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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​Vocabulary

​If x is the independent variable and y is the dependent variable, then you can use function notation to write y=f(x), which is read "y equals f of x", where f names the function.

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When an equation in two variables describes a function, you always can use function notation to write it.

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Fill in the Blanks

The _____ depends on the ____.

Fill in the Blanks

Name the dependent variable:

Fill in the Blanks

Write an equation in function notation for the total amount of money that Kate earns for h hours worked.

Fill in the Blanks

How much money will she earn after working 8 hours?

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Multiple Choice

Find a reasonable domain for this function.

• D: {1, 2, 3, 4, 5}

• D: {0, 1, 2, 3, 4, 5}

• D: {17, 19, 21, 23, 25, 27}

Multiple Choice

Find a reasonable range for this function.

• R: {1, 2, 3, 4, 5}

• R: {0, 1, 2, 3, 4, 5}

• R: {17, 19, 21, 23, 25, 27}

Multiple Choice

Write a function for the temperature in degrees Celsius.

• f(h) = 17h + 2

• f(h) = 17 + 2h

Open Ended

Find a reasonable domain for this function.

Open Ended

Find a reasonable range for this function.

Open Ended

Write a function for Takumi's total earnings.

Open Ended

How can you identify the independent variable and the dependent variable given a situation?