A slant asymptote is represented in a graph with a diagonal or slant dotted line since its equation is y=mx+b. A slant asymptote only exists when the degree on the numerator is one more bigger than the degree than the denominator. For example the function x^3+4/x^2-5 would represent a slant asymptote. In order to find the equation of a slant asymptote we have to perform long division and everything we get as a result except for the remainder is the equation for this asymptote.For example if we performed long division for a function and got x+2 remainder 5; the equation for the slant asymptote would only be x+2 without the remainder. For slant asymptotes that graph can sometimes cross the slant asymptote towards the middle.
Monday, September 24, 2012
Unit G Summary Questions #3: Slant Asymptotes
3. When does a graph have a slant asymptote? How do you find the equation of the slant asymptote?
A slant asymptote is represented in a graph with a diagonal or slant dotted line since its equation is y=mx+b. A slant asymptote only exists when the degree on the numerator is one more bigger than the degree than the denominator. For example the function x^3+4/x^2-5 would represent a slant asymptote. In order to find the equation of a slant asymptote we have to perform long division and everything we get as a result except for the remainder is the equation for this asymptote.For example if we performed long division for a function and got x+2 remainder 5; the equation for the slant asymptote would only be x+2 without the remainder. For slant asymptotes that graph can sometimes cross the slant asymptote towards the middle.
A slant asymptote is represented in a graph with a diagonal or slant dotted line since its equation is y=mx+b. A slant asymptote only exists when the degree on the numerator is one more bigger than the degree than the denominator. For example the function x^3+4/x^2-5 would represent a slant asymptote. In order to find the equation of a slant asymptote we have to perform long division and everything we get as a result except for the remainder is the equation for this asymptote.For example if we performed long division for a function and got x+2 remainder 5; the equation for the slant asymptote would only be x+2 without the remainder. For slant asymptotes that graph can sometimes cross the slant asymptote towards the middle.
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