Pg. 149 Homework• Pg. 149 #2 – 23 (every 3rd problem)

Pg. 151 # 50 - 57

• #1 [-5, 5] by [-2, 10]• #4 [-4, 4] by [-10, 10] • #7 [-1,000, 3,000] by [-15,000,000, 2,000,000]• #10 minimum = (3/14, 831/28)• #13 Zeros = maximum = (0, 10)• #16 Intercept = (1.30, 0) and no maxima• #19 Zeros = (3.81, 0) Max = (0.33, -29.85)

Min = (1, -30)• #22 Zeros = (0, 0), (4, 0), (22, 0) Max = (1.79, 145,74)

Min = (8.21, -385.74)

10,0 , 10,0

3.1 Graphs of Polynomial Functions

Definition • A polynomial function is

one that can be written in the form:

where n is a nonnegative integer and the coefficients are real numbers. If the leading coefficient is not zero, then n is the degree of the polynomial.

State whether the following are polynomials. If so, state the degree.

11 1 0...n n

n nf x a x a x a x a

27

3f x x

3 2 1f x x x x

5 4 3 22 3 5 4 10f x x x x x

2 1f x x

121f x x x x

3.1 Graphs of Polynomial Functions

End Behavior• End behavior is determined

by the degree and the leading coefficient.

• Create Chart.

Number of “Bumps”• The number of “bumps” a

graph may have is no more than one less than the degree.

• The number of zeros a graph may have is no more than the number of the degree.

2 3 10f x x x

4 3 22 3 3f x x x x

2.7 Inverse Functions

Inverse Functions• Show that f(x) =

will have an inverse function. – Find the inverse function and

state its domain and range. – Prove that the two are

actually inverses.

• Show that g(x) = will have an inverse function. – Find the inverse function and

state its domain and range. – Prove that the two are

actually inverses.

• Will h(x) = x2 – 2xwill have an inverse function?

3 1x 2

1x

2.6 Relations and Parametric Equations

Circles• Write the following

equation of a circle in standard form and state the center and radius.

Symmetry• Determine the type of

symmetry, if any, of the equations below.

2 2 6 8 0x y x y 3 3 4xy x y

3 5f x x x