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

Pg. 151 # 50 - 57Study for Quiz: Sections 2.5 – 2.7

• #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

2.5 Solving Higher Order Inequalities Algebraically and Graphically

Sign Patterns• Create a sign pattern to

solve the following inequalities:

Solving Inequalities Algebraically

• Solve the following inequalities algebraically:

22 5 3x x 2x x

1 4 1 11

4 12 6

x

5 3 2x

2.5 Solving Higher Order Inequalities Algebraically and Graphically

Solving Inequalities Graphically

• Solve the following inequalities graphically:

Word Problems!!• A swimming pool with

dimensions of 20 by 30 ft is surrounded by a sidewalk of uniform width x. Find the possible widths of the sidewalk if the total area of the sidewalk is to be greater than 200 sq ft but less than 360 sq ft.

3 29 6 55 0x x x

2 1 2 3x x

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

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.

• Show that h(x) = x2 – 2xwill have an inverse function.

3 1x 2

1x

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

5 9f x x

22 9 3f x x x

6 4 3 23 7 2 5 9f x x x x x

2 9f 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.

22 9 3f x x x

5 4 3 23 7 2 5 9f x x x x x