DO NOW!!!Simplify the following rational expressions:1. 2.

3.

Graphing Rational Functions

Vertical Asymptote: a vertical line that a rational function approaches but can never actually cross• Expressed as x = “?” lines• We find vertical asymptotes by

finding the values where the denominator of a rational function equals ZERO.

Graphing Rational Functions

Horizontal Asymptote: a horizontal line that a rational function approaches but can never actually cross• Expressed as y = “?” lines

Finding Horizontal Asymptotes

1. If the numerator has a lower highest power then the denominator, the HA is at the line y = 0.

2. If the numerator and the denominator have the same highest power, divide the leading coefficients to find the HA.

3. If the numerator has a higher highest power than the denominator, then the function has no horizontal asymptote.

X and Y-Intercepts!!!• To find the y-intercept, plug in “0” for

“x”.

• To find the x-intercept, set the numerator of the fraction equal to “0” and

Examples!!!For the following functions:a) Find the x and y-intercepts.b) Find the vertical asymptote.c) Find the horizontal asymptote.

1.

THINK!?!?

It takes Amir 7 more minutes than Mr. Hammer to solve a really hard math problem. Together, they can complete the math problem in 12 minutes. How long does it take Amir to complete the problem on his own?