GRAPHING SIMPLE RATIONAL FUNCTIONS. Investigation Graph the following using the normal window range. Draw a rough sketch of these functions on the back.

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Presentation transcript:

GRAPHING SIMPLE RATIONAL FUNCTIONS

Investigation Graph the following using the normal window range. Draw a rough sketch of these functions on the back of page 5 in your packet: 1. Y = 3/X2. Y = 6/X 3. Y = -8/X4. Y = -4/X What do you notice?!?!?

Rational Function There are 2 forms of a rational function 1) 2) Where p(x) & q(x) are polynomials (Inverse Variation)

Rational functions in the form y = k/x are split into parts. Each part is called a BRANCH. branch

Asymptotes An Asymptote is a line (vertical or horizontal) that the graph approaches but NEVER touches!

Asymptotes

What’s domain? The domain of a function is the set of all possible x-values. Vertical Asymptotes are values not included in the domain

What’s range? The range of a function is the set of all possible y-values. Horizontal Asymptotes are values not included in the range

Asymptotes for Inverse Variation: From the form the Vertical Asymptote is when you set x – b = 0 and solve (how you move the graph left or right) the Horizontal Asymptote is y = c (how you move the graph up or down) k has no influence on the asymptotes.

Identifying Asymptotes Identify the Asymptotes from the following functions. State the Domain and Range. 1.

Identifying Asymptotes Identify the Asymptotes from the following functions. State the Domain and Range. 2.

Identifying Asymptotes Identify the Asymptotes from the following functions. State the Domain and Range. 3.

4. What would an equation of a rational function look like if it had a H.A. of y = -4 and a V.A. of x = -2 State the Domain and Range

RATIONAL FUNCTIONS

A rational function is a function of the form: where p and q are polynomials

Vertical Asymptotes REMEMBER! To find a vertical Asymptote, set the bottom equal to zero and solve!

State the VA, and the domain?

Asymptotes What are the Asymptotes? Graph it, what do you notice?!

Holes A HOLE in the graph is when (x – a) is a factor in both the numerator and the denominator. So on the graph, there is a HOLE at 4.

Find VA, Holes and State Domain

WHATS MISSING?!?!? To find the Horizontal Aysmptotes for rational functions: Determine the degree of the numerator and the denominator.

Horizontal Asymptotes To find a horizontal asymptotes, we focus on the degree of the numerator and the denominator. What’s the degree?

How do we use degrees to find the horizontal asymptote?

Degree of 3 Degree of 5 The degree is bigger on the bottom, so the horizontal asymptote is the line y = 0.

Degree of 6 Degree of 1 The degree is bigger on the top, so there is no horizontal asymptote.

Degree of 1 The degrees are the same, so divide the leading coefficients. The horizontal asymptote is y = 2.

Find it all! Vertical and Horizontal Asymptote and Holes and State Domain and Range