APPC QUICK REVIEW!

I’ve got a test in AP Precalculus in about an hour, so it’s time for a quick review!!

Holes

(x)(x+3)/(x+3)(x+4)

Holes are the numbers that can be simplified from the top and bottom of a polynomial function. So, (x+3) can be eliminated from top and bottom, making a hole at (-3,?). To find the y-value, plug the x-value in the simplified equation.

(x)/(x+4) --> (-3)/(-3+4) --> -3/1 --> y value = -3

Vertical Asymptotes

(x)(x+3)/(x+3)(x+4)

x=-4 would be a vertical asymptote as it is on the bottom of the polynomial function and not a hole. Vertical asymptotes are lines in the function that x approaches, but never quite hits. Holes always dominate Vertical asymptotes.

Horizontal Asymptotes/End Behavior

num. > den.

For this, there is no horizontal asymptote but rather a slant asymptote. For this, look at the signs of the top and bottom to see if it goes to positive or negative infinity.

num. = den.

The horizontal asymptote is the num/den.

3x+3/2x+2 --> y = 3/2

num. > den.

The horizontal asymptote is at y=0.

The Roots

The zeros/roots are the numbers on the top that aren’t holes.

(x)(x+3)/(x+3)(x+4) --> x = 0 is the root

Reflection

Wish me luck on my test, thank you for reading!