How do you graph #f(x)=(x2)/(x4)# using holes, vertical and horizontal asymptotes, x and y intercepts?
Undefined at
See explanation for the rest
Hole is where the denominator becomes 0. The function becomes undefined at that point. So for this condition we have
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lets consider the behaviour close to
If
If
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
As
As
By signing up, you agree to our Terms of Service and Privacy Policy
To graph the function f(x) = (x2)/(x4), follow these steps:

Determine the vertical asymptote: Set the denominator (x4) equal to zero and solve for x. The vertical asymptote is x = 4.

Identify any holes: Simplify the function by canceling out common factors between the numerator and denominator. If any factors cancel out, there will be a hole at that xvalue. In this case, there are no common factors to cancel out, so there are no holes.

Find the xintercept: Set the numerator (x2) equal to zero and solve for x. The xintercept is x = 2.

Find the yintercept: Substitute x = 0 into the function and solve for y. The yintercept is (0, 1/2).

Determine the horizontal asymptote: Compare the degrees of the numerator and denominator. Since they have the same degree (1), divide the leading coefficients. The horizontal asymptote is y = 1.

Plot the points: Plot the xintercept, yintercept, and any other desired points on the graph.

Draw the graph: Connect the points smoothly, approaching the vertical asymptote at x = 4 and the horizontal asymptote at y = 1.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7