1. A. Give the equation of each vertical asymptote, and give the corresponding factor that will appear in the rational function. vertical asymptote factor Should these factors appear in the numerator or denominator of function? B. Give each x-intercept of the function, tell whether the graph crosses or touches the x-axis, give the corresponding factor that will appear in the rational function, and tell whether the power will be even or odd. x-intercept cross/touch factor odd/even power Should these factors appear in the numerator or denominator of the function?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Rational Functions And Conics
Section4.2: Graphs Of Rational Functions
Problem 51E: In this question, (a) state the domain of the function, (b) identify all intercepts, (c) find any...
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C. Using your information from A and B, form a trial function. Write that function below.
Now use your calculator to test it visually, setting your caleulator so that the viewing window
matches the grid of the graph. Do you need to change any powers or multiply the numerator by -
1 to make your graph look more like the one given? If so, make the necessary change(s) and show
your modified funetion below.
Continue checking your function algebraically, as follows:
i) What y-intercept does your function have?
Is it the same as the y-intercept of graph given?
If not, modify your function to make them match (without changing the x-intercepts or the
vertical asymptotes) and show the modified function below.
ii) What is the horizontal asymptote for your function?
Does the graph given have the same horizontal asymptote?
If not, modify your function to make them match (without changing the x-intercepts and the
vertical asymptotes) and show the modified function below.
D. Write your final function here:
Transcribed Image Text:C. Using your information from A and B, form a trial function. Write that function below. Now use your calculator to test it visually, setting your caleulator so that the viewing window matches the grid of the graph. Do you need to change any powers or multiply the numerator by - 1 to make your graph look more like the one given? If so, make the necessary change(s) and show your modified funetion below. Continue checking your function algebraically, as follows: i) What y-intercept does your function have? Is it the same as the y-intercept of graph given? If not, modify your function to make them match (without changing the x-intercepts or the vertical asymptotes) and show the modified function below. ii) What is the horizontal asymptote for your function? Does the graph given have the same horizontal asymptote? If not, modify your function to make them match (without changing the x-intercepts and the vertical asymptotes) and show the modified function below. D. Write your final function here:
1.
A. Give the equation of each vertical asymptote, and give the corresponding factor that will
appear in the rational function.
vertical asymptote
factor
Should these factors appear in the numerator or denominator of function?
B. Give each x-intercept of the function, tell whether the graph crosses or touches the x-axis, give
the corresponding factor that will appear in the rational function, and tell whether the power will
be even or odd.
x-intercept
cross/touch
factor
odd/even power
Should these factors appear in the numerator or denominator of the function?
Transcribed Image Text:1. A. Give the equation of each vertical asymptote, and give the corresponding factor that will appear in the rational function. vertical asymptote factor Should these factors appear in the numerator or denominator of function? B. Give each x-intercept of the function, tell whether the graph crosses or touches the x-axis, give the corresponding factor that will appear in the rational function, and tell whether the power will be even or odd. x-intercept cross/touch factor odd/even power Should these factors appear in the numerator or denominator of the function?
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