DO NOW!!! Simplify the following rational expressions: 1. 2. 3.

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Presentation transcript:

DO NOW!!! Simplify the following rational expressions:

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!!!

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?