Precalc Unit 2

When the degree of the denominator is larger than the degree of the numerator (Bigger on Bottom) 

horizontal asymptote: y = 0 ———> both limit notations equal 0 

When the degrees are the same for both num and denom. (BOSCO)

horizontal asymptote: y = 2x/x—> 2 

when the degree of the numer. is larger than denom. and there is no horizontal asymptote (Bigger On Top)

no horizontal asymptote

If the degree of numer. is exactly one more than the degree of the denominator

slant/oblique asymptote and to find, you divide the quotient by the divisor

zero

coordinate on x-axis—> (5,0) 

An x-intercept occurs at the value that makes the…

function equal ZERO (numerator = 0)

A vertical asymptote occurs when a factor in the…

denominator cannot cancel out with the factors in the numerator that makes the DENOMINATOR ZERO (number that makes denominator = zero, and does not cancel with numer.)

A hole or removable discontinuity..

when a factor in the denominator cancels out with a factor in the numerator at the value of x—> makes both the numerator and denominator zero 0

To find the hole coordinate—> plug in the x value of hole to equation 

When taking out an x of the equation..

that x will be 0—→ 1/ x

When doing limit notation..

use the vertical asymptotes to determine the