Graphing Simple Rational Functions
Investigation Graph the following: 1. Y = 3/X 2. Y = 6/X 3. Y = -8/X 4. Y = -4/X What do you notice?!?!?
Rational Function There are 2 basic forms of a rational function 1) 2) Where p(x) & q(x) are polynomials
Rational functions in the form y = are split into parts. Each part is called a BRANCH. To see the direction of your branches look in your calculator and sketch.
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 From the form the Vertical Asymptote is when you set x – b = 0 and solve the Horizontal Asymptote is y = c
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 k=2, it had a H.A. of y = -4, and a V.A. of x = -2 State the Domain and Range Then sketch the graph.