SOLUTION: Identify the horizontal and vertical asymptotes and the intercepts for the function and then
graph:
𝑓(𝑥) = (3𝑥^2)/((𝑥^2)−7𝑥+12)
Algebra ->
Rational-functions
-> SOLUTION: Identify the horizontal and vertical asymptotes and the intercepts for the function and then
graph:
𝑓(𝑥) = (3𝑥^2)/((𝑥^2)−7𝑥+12)
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Question 1125467: Identify the horizontal and vertical asymptotes and the intercepts for the function and then
graph:
𝑓(𝑥) = (3𝑥^2)/((𝑥^2)−7𝑥+12) Answer by solver91311(24713) (Show Source):
You have a rational function where the degree of the numerator polynomial is equal to the degree of the denominator polynomial. The horizontal asymptote of such a function is equal to the ratio of the lead coefficient of the numerator to the lead coefficient of the denominator.
A vertical asymptote exists at any value of the independent variable that makes the denominator equal to zero. Find all zeros of the denominator polynomial.
The -intercept is at the value of the function when . Substitute for and do the arithmetic.
An -intercept exists at any value of the independent variable that makes the numerator polynomial equal to zero.
As an aid to graphing this note that your denominator is a quadratic that has a positive discriminant, therefore it has two distinct real roots. Use these two roots to divide the -axis into three open intervals. Select a value from each of the intervals and evaluate the entire function at that value. Note the sign of the function value in that interval which will be the sign of the function anywhere in that open interval. You also might want to graph this in a piece-wise fashion with different scales for different parts of the graph. If you zoom out far enough to see one part of it, you lose important detail in another part.
John
My calculator said it, I believe it, that settles it
