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Notes Over 2.2 1 3 5 8 7 Identifying Functions - Numerically Decide whether the relation is a function. 1. Input Output A function , because every input goes to only one output Not a function , because 4 goes to both 3 and 5

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Notes Over 2.2

  • 1

  • 3

  • 5

  • 8 7

Identifying Functions - Numerically

Decide whether the relation is a function.

1. Input Output

A function, because every input goes to only one output

Not a function, because 4 goes to both 3 and 5


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Notes Over 2.2

Identifying Functions - Verbally

Decide whether the relation is a function.

  • In a school basketball game, all ticket prices are the same. The input value x is the number of tickets purchased, and the output y is the total price paid.

A function, because every input goes to only one output

  • The input value x is the number of times you cast your line in fishing, and the output y is the total number of fish caught.

Not a function, because you could throw your line in 5 times one day and catch 2 fish and another day throw it in 5 times and not catch anything.


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Notes Over 2.2

Identifying Functions - Graphically

Decide whether the relation is a function.

5.

Vertical line test

A function, because it only hits the graph once all the way across.


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Notes Over 2.2

Identifying Functions - Graphically

Decide whether the relation is a function.

6.

Vertical line test

Not a function, because it hits the graph more than once from -5 to 5.


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Notes Over 2.2

Identifying Functions - Algebraically

Decide whether the relation is a function.

Try to solve for y

A function, because every input goes to only one output

Not a function, because most inputs will have 2 outputs


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Identifying Functions

Find f(-2), f(5), and f(x - 3)


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Notes Over 2.2

Evaluating a Piecewise Function

Evaluate the function for the given value of x.


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Notes Over 2.2

Finding the Domain of a Function

Find the domain of each function.

Domain excludes x-values that result in division by 0.

Domain excludes x-values that result in even roots of negative numbers.

All real numbers


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Notes Over 2.2

l l l l l l l l l l l l l

-6 -4 -2 0 2 4 6

Finding the Domain of a Function

Find the domain of each function.

Closed Circles

These are critical values


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Notes Over 2.2

Function Application

  • Andre Agassi hit a lob in tennis right on his baseline that took a path given by the function:

where x and y are measured in feet. If a tennis court is 78 feet long, will the ball land in, assuming he hit it straight?

No, because it is still coming down.



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