Warm up

1. Warm up Is this the Graph of a Function? State the Domain. State the Range. Where is y= f(x) Increasing? Where is y=f( x) Decreasing? Where is y=f(x) Constant?

2. Zeros of a Function • The Zeros of a function f(x)are the values of x that make f(x)=0. Zeros can be real or complex. steps to find zeros : • Set the equation=0 • Solve for the independent variable (x)

3. Examples Find the Zeros of the following functions: 1. 2. 3.f(x)=

4. Examples/guided practice 4.Find the zeros of: Try These:

5. Writing a linear function • A linear function of x is of the form f(x)=mx+b Example 1: Write a linear function for which f(1)=4, f(0)=6 Step 1: since f(x) is the same as y, f(1)=4 implies x=1 and y=4; f(0)=6 implies x=0 and y=6 Step 2: find an equation of the line passing through the points (1,4) and (0,6) Step 3: replace y with f(x). Check your result .

6. More examples/ practice • Write the linear function for which: • f(-10)=12, f(16)=-1 2. , • Practice Problems: Write linear functions for the following function values: 1.f(5)=-4, f(-2)=17 2.f(-3)=-8, f(1)=2 3. ,

7. Even and Odd Functions Graphically: Even functions: are Functions whose graphs are symmetric with respect to the y-axis Odd Functions: are functions whose graphs are symmetric with respect to the origin

8. Explorations • Graph each function using a graphing calculator and determine whether the function is even, odd or neither: • what do you notice • about functions that • are odd? Even? • How can you • identify even and • odd functions by • inspecting the eqn.?

9. Even and odd functions Contd. • Algebraically: A function f(x)is EVEN if f(-x)=f(x) A Function f(x) is ODD f(-x)= -f(x) Examples: determine if the following functions are even, odd or neither: 1. 2. 3.

10. practice • Determine if the following functions are even, odd or neither algebraically: