How do you graph #f(x)=(2x^2)/(x3)# using holes, vertical and horizontal asymptotes, x and y intercepts?
Now let's see about the Horizontal asymptote.
I like to use this to help me remember:
BOBO  Bigger on bottom, y=0
BOTN  Bigger on top, none
EATS DC  Exponents are the same, divide coefficients
So in our case, the numerator (top) has a greater exponent (bigger). So there is no Horizontal asmptote (BOTN)
Now we have all the information we need
To check our answers, let's graph the equation graph{y=(2x^2)/(x3)}
Our math is correct. Good job
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To graph the function f(x) = (2x^2)/(x3), we can follow these steps:

Determine the vertical asymptote: Set the denominator (x3) equal to zero and solve for x. The resulting value of x (in this case, x = 3) gives us the vertical asymptote.

Identify any holes in the graph: Check if there are any common factors between the numerator (2x^2) and the denominator (x3). If there are, cancel them out and determine the xvalues where the function is undefined. These xvalues represent holes in the graph.

Find the horizontal asymptote: Determine the degree of the numerator and the denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degrees are equal, divide the leading coefficients of the numerator and denominator to find the horizontal asymptote. If the degree of the numerator is greater, there is no horizontal asymptote.

Calculate the xintercepts: Set the numerator (2x^2) equal to zero and solve for x. The resulting values of x represent the xintercepts.

Calculate the yintercept: Substitute x = 0 into the function f(x) and solve for y. The resulting value of y represents the yintercept.
Using these steps, you can graph the function f(x) = (2x^2)/(x3) accurately, indicating the holes, vertical and horizontal asymptotes, as well as the x and y intercepts.
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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.
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