UNIT 4Polynomials and other functions

Graphing PolynomialsCan you find the end behavior?Can you identify the zeros, roots, x-

intercepts, or solutions?Can you identify where the function is

increasing or decreasing?Can you find the extrema, the maximumsand the minimums?Can you identify the domain and range?

What do I know about the degree of a function?Look at the arms of the graph.Player 15 is modeling an even oran odd function?

It is an even function.

What kind of a function is player 62 modeling?It is an odd function.Since player 62 has his left arm up, then what do you know about the lead coefficient of this function?It is a negative number.

What is the relationship between the roots and the factors of a polynomial function?

The factor is written as the opposite of the root.

Example if the root is -3, then the factor is (x + 3).

Example if the root is 7, then the factor is (x – 7)

How do I find all of the zeros?First graph and find the real roots.

If you still need more roots, then use synthetic division.

Until you can use the quadratic formula

What is a rational equation?A rational equation is basically a polynomial divided by a polynomial.

Examples:

Graphic examples of rationals.http://www.wyzant.com/resourc

es/lessons/math/algebra/rational_expressions

How do I find the holes of a rational equation?Factor the numerator and the denominator.

If a factor cancels top and bottom, then this factor will create a hole.

Set the factor equal to zero and solve.This is a hole.

What is an asymptote?It is a line the graph approaches, but never touches.

How do I find the vertical asymptotes of a rational equation?Factor the numerator and the denominator.

Any factors remaining in the denominator will be vertical asymptotes.

Set each factor equal to zero, then solve.This is your vertical asymptote(s).

How do I find the horizontal asymptotes of a rational equation?Look at the highest degree of the numerator and the

denominator.Rule 1: If the degree on the top is highest, then there is

not a horizontal asymptote.Rule 2: If the degree on the bottom is highest, then the

horizontal asymptote is y = 0.Rule 3: If the degrees are the same, then it is y= the

numerator coefficient divided by the denominator coefficient of the highest degrees.

How would you solve the following? Discuss with your group and try to solve the equation. Check your answer to see if it is correct.

𝑦𝑦+1

=23

How would you solve the following? Discuss with your group and try to solve the equation. Check your answer to see if it is correct.

=+

Adding RationalsYou must have a common denominator to add fractions.

You might or probably will need to factor the denominators to find the LCD. (You don’t need to factor the numerators!)

Creating an open box by cutting squares from each corner of a rectangle.What is the volume formula for the box?V(x) = (length – 2x)(width – 2x)x, where x is the

side of the square to be cut. X is also the height of the box.

How do you find the domain?It is from 0 to half the shortest side of the

rectangle.How do you graph the volume.Set the window x-min, then x-max, then zoom 0.