HOMEWORK: WB p.31 (don’t graph!) & p.34 #1-4

RATIONAL FUNCTIONS: HORIZONTAL ASYMPTOTES & INTERCEPTS

REMOVABLE DISCONTINUITY (HOLE)

VERTICAL ASYMPTOTES:

DOMAIN What is going to affect the domain of our functions? -Removable discontinuities -Vertical asymptotes

PUT IT ALL TOGETHER! Find all holes, vertical asymptotes, and the domain for each problem.

X-INTERCEPTS: The points of intersection between a graph and the x-axis Every x-intercept has the same form of (x,0). To solve for an x-intercept, we set y = 0 and solve for x. The points of intersection between a graph and the y-axis Every y-intercept has the same form of (0,y). To solve for a y-intercept, we set x = 0 and solve for y. Y-INTERCEPTS:

PRACTICE! PRACTICE! PRACTICE!

MOST “SIGNIFICANT” TERM When x is VERY large, what is the most significant term of:

MOST “SIGNIFICANT” TERM When x is VERY large, what is the most significant term of:

HORIZONTAL ASYMPTOTES: When the end behavior of a graph approaches a specific y-value Case 1: the degree of the numerator polynomial is LESS THAN the degree of the denominator polynomial Result: the horizontal asymptote is y = 0 Case 2: the degree of the numerator polynomial is EQUAL to the degree of the denominator polynomial Result: the horizontal asymptote is the ratio of the leading coefficients Case 3: the degree of the numerator polynomial is GREATER THAN to the degree of the denominator polynomial Result: there is no horizontal asymptote. Instead, there is a slant asymptote

PUT IT ALL TOGETHER! Identify all holes, asymptotes, intercepts, and state the domain.