1. 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

2. 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.

3. 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.

4. 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.

5. 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

6. Notes Over 2.2 Identifying Functions Find f(-2), f(5), and f(x - 3)

7. Notes Over 2.2 Evaluating a Piecewise Function Evaluate the function for the given value of x.

8. 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

9. 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

10. 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.

11. Notes Over 2.2