Explain how to find the vertical asymptote(s) of a rational function. When does
ID: 3114988 • Letter: E
Question
Explain how to find the vertical asymptote(s) of a rational function. When does a rational function not have a vertical asymptote? When does a rational function have the horizontal asymptote y = 0? When does a rational function have the horizontal asymptote y = leading coefficient of the numerator /leading coefficient of the denominator? When does a rational function have a slant asymptote? When does a rational function have no horizontal asymptote and no slant asymptote? 1. 2. 3. 4. . When does a rational function have a hole in its graph? 6. Let f(x)= x2-4 a. List what kind of symmetry the graph has, if any b. Give the x-intercepts, if any. Give the y-intercept, if any. Give your answers as ordered pairs. c. Give the vertical asymptotes, if any. Give your answers as equations of lines d. Give the horizontal asymptote, if any. Give your answer as an equation of a line e. Graph fby hand.Explanation / Answer
1)for rational function vertical asympototes are zeros of the denominator(undefined points) of simplified function
to find out just equate denominator to zero
2)if denominator degree> numerator degree the horizontal asymptote is x-axis that is y=0
3) if numerator degree = denominator degree ( degree are equal ) the asymptote y=numerator leading cofficent/denominator leading co efficent
4)if numerator degree>1+denominatr degree then there is no horizontal asymptote
A slant asymptote occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator.
if numerator degree less than denominator degree no slant asymptote
as per chegg rule 4 question are answered
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