Warm up:

Notes 7.2: Graphing Rational Functions

What is a rational function? Basically, a rational function is a fraction with polynomials for numerators and denominators. The inverse variation function is a rational function. The graph: the graphs of rational functions have both a vertical AND horizontal asymptote. There are two curved lines on the graph. Domain and Range: They are both infinity, with the only exclusions being the horizontal and vertical asymptotes. Table: choose three values on either side of the vertical asymptote

Let’s graph… 1) f(x) =2) g(x) =

Translating rational graphs:

In a nutshell…..  “a” is the vertical stretch of the graph  “h” is the shift left or right, also the vertical asymptote (remember, x’s lie!)  “k” is the shift up or down, also the horizontal asymptote.  a negative touching the “a” is a reflection over the x – axis.

Let’s graph: A) m(x) =B) w(x) =

What if we don’t have “standard form?”  You need to know the following if we DON’T have standard form, rather the form is:  The vertical asymptote is found by solving cx + d = 0.  The horizontal asymptote is found by

Let’s try some: 1)2)

HW: p. 370#3 – 17 odd, 19 – 24 all

Warm up:

Rewrite and Graph a Rational Function What if our rational function is not in form? We have to rewrite it! 1) Divide the numerator by the denominator 2) The remainder goes in place of “a” The divisor goes in place of “x – h” The dividend goes in place of “k”

Let’s try a couple: 1) 2) 3)

Now, let’s graph 1) 2)

DUE in CLASS: p. 371 #