Y=X2+2x-8 over X2-3x+2

Question

Need x intercept

vertical asymtope

horizontal asmytope

holes

table of values 

Answer 1

If this is your problem, it is reasonable to assume that you are in an Algebra II or College Algebra course, where a textbook would present a summary of all that must be done to analyze a rational algebraic function, along with numerous fully worked examples.

 

The analysis is based on factoring both the numerator & denominator. Any zeros of the denominator are excluded from the domain. THEN any matching factors in num. & denom. can cancel; these will be associated with holes.

 

Every remaining factor in the denominator correlates to a vertical asymptote.

 

If the degree of the denominator exceeds that of the numerator then the line y=0 is an horizontal asymptote.

If the degrees of num. & denom. are equal, then y = constant is an horizontal asymptote, k being the ratio of leading coefficient of num. to leading coeff. of denom.

 

If degree of num. is exactly equal to 1+denom. degree, then doing long division will identify the slant asymptote.

 

the y intercept (one at most) is found by substituting x=0. The x intercepts are determined by setting the NUMERATOR to 0.

 

There's work to do..get going!