How do you identify the zeroes and asymptotesof #f(x) = (4x^2-16)/(x^2-9)#?
1 Answer
Let me split this up
Explanation:
To find zeros, it means to find x-intercepts, i.e. where
In this case, when
Assuming
Verifying that
Therefore,
To find asymptotes, we have to find the x and y values as y and x tend to infinity. Let me split this up into horizontal and vertical asymptotes:
Horizontal asymptote is the y-value as
Dividing the numerator and denominator by the variable with the highest power, i.e.
As the variable in the fraction is a squared variable, it means that
Therefore, the horizontal asymptote is
Vertical asymptotes are x-values that cause the function to carry a not well defined value or indeterminate form, such as
This means that at