24-25 | Graphing Radicals and Quadratics | PreCalc

Radical Fin.: How do you find Zeros?

Make the numerator zero

Radical Def.: What is a Zero?

Where it intercepts the X axis

Radical Ex.: What are the Zeros in f(x) = (x+2)/(x+3)

There is one at x = -2

Radical Fin.: How do you find a Y Intercept?

Set the function to f(0)

Radical Def.: What is a Y intercept

Where it intercepts the Y axis

Radical Ex.: Find Y Intercept of f(x) = (x+2)/(x-3)

f(0) = (0+2)/(0+3) = 2/3

Radical Fin.: Holes

When the same term is on the top and bottom

Radical Def.: What are holes

The function is not true there, denotated with a donut on the line

—o—

Radical Ex.: find the hole in f(x) = (x+3)(x-5)/(x+3)

x = -3

Radical Fin. Vertical Asymptote

When the bottom term = 0

Radical Def.: Vertical Asymtote

Function approaches infinity/-infinity as it approaches this number, its a vertical line

Radical Ex.: Find the Vertical Asymptote in f(x) = (x+2)/(x+3)

-3

Radical Fin.: How do you find the horizontal asymptote

Divide the constant of the highest degree in the numerator by the constant of the highest degree in the denominator.

Radical Def: horizontal asymtote

Function approaches infinity/-infinity as it approaches this number, its a horizontal line

Radical Ex.: Find the horizontal asymptote for f(x) = (3x+6)/(2x+1)

3/2

Polynomial Fin.: Degree

Highest exponent when foil’d

Polynomial def.: degree

When odd, end behavior will be either / or \, when even, it will be V or ^.

Polynomial Ex.: find degree of f(x) = (x+2)²(-x+1)³

5

Polynomial fin.: Sign orientation

What the sign is of the foil’d equation

Polynomial Def. sign orientation

The graph will end / or V if positive, and will end \ or ^ if negative

Polynomial Ex.: What is the sign orientation of f(x) = (x-3)(x+2)

f(x) = x²-x-6, Positive