How do you graph #f(x)=(x1)/x^2# using holes, vertical and horizontal asymptotes, x and y intercepts?
See answer below
This type of equation is called a rational (fraction) function.
Step 1 factor : The given function is already factored.
Step 4, find horizontal asymptotes: Compare the degrees:
graph{(x1)/x^2 [10, 10, 5, 5]}
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To graph the function f(x) = (x1)/x^2, we can analyze its key features:

Holes: The function has a hole at x = 1, as the denominator becomes zero at this point. To find the ycoordinate of the hole, substitute x = 1 into the function.

Vertical Asymptotes: The function has a vertical asymptote at x = 0, as the denominator approaches zero as x approaches 0. To determine the behavior of the function as x approaches positive or negative infinity, analyze the degrees of the numerator and denominator.

Horizontal Asymptotes: To find the horizontal asymptote(s), compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, divide the leading coefficients to find the horizontal asymptote. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

xintercepts: To find the xintercept(s), set f(x) = 0 and solve the resulting equation.

yintercept: To find the yintercept, substitute x = 0 into the function.
By analyzing these features, you can accurately graph the function f(x) = (x1)/x^2.
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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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