The end behavior of f(x)=(2+x^2)/(x^2-36) most closely matches which of the following:
y=1
y=-1
y=2
y=0
There is no leading coefficient so I am not sure what the answer is.
CORRECTION: THE SECOND OPTION IS NOT Y=-1 it is Y=-18
The end behavior of f(x)=(2+x^2)/(x^2-36) most closely matches which of the following:
y=1
y=-18
y=2
y=0
as x gets huge, the 2 and the 36 become insignificant:
y -> x^2/x^2
so the answer is 2?
since when is x^2/x^2 = 2?
10/10 = 1
z^3/z^3 = 1
don't forget your Algebra I now that you're taking calculus.
Using the usual method, divide top and bottom by x^2. That gives you
(1 + 2/x^2)/(1 - 36/x^2)
as x^2 gets huge, 1/x^2 -> 0
and the fraction becomes 1/1
NOT 2!!
ok THANK YOU!!!!!!!
To determine the end behavior of a rational function, you need to look at the degrees of the numerator and denominator. In this case, the numerator is a polynomial of degree 2 (since it includes the term x^2) and the denominator is also a polynomial of degree 2 (since it includes the term x^2).
Since the degrees of the numerator and denominator are the same, this means that the end behavior of the function is determined by the ratio of the leading coefficients of the numerator and denominator. In other words, you need to compare the coefficients in front of the highest degree terms.
For the numerator, the leading coefficient is 1 (since there is no coefficient explicitly written). For the denominator, the leading coefficient is also 1 (since x^2 - 36 can be rewritten as 1*x^2 - 36).
Therefore, the ratio of the leading coefficients is 1/1, which simplifies to 1. This means that as x approaches positive or negative infinity, the function f(x) approaches the value of 1.
So, the end behavior of f(x)=(2+x^2)/(x^2-36) most closely matches y=1.