How do you graph #f(x)=(1x^2)/x# using holes, vertical and horizontal asymptotes, x and y intercepts?
no holes
vertical asymptote at
no horizontal asymptote
slant/oblique asymptote at
Holes: Since there are no terms that cancel, there are no holes.
You need to use long division to find the slant/oblique asymptote :
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To graph the function f(x) = (1  x^2)/x, we can analyze its properties:

Holes: The function has a hole at x = 0 since the denominator becomes zero, resulting in an undefined value.

Vertical asymptotes: As x approaches positive or negative infinity, the function approaches positive or negative infinity, respectively. Therefore, there are vertical asymptotes at x = ∞ and x = +∞.

Horizontal asymptote: To find the horizontal asymptote, we examine the behavior of the function as x approaches positive or negative infinity. By dividing the highest power of x in the numerator and denominator, we see that the degree of the numerator is 2 and the degree of the denominator is 1. Thus, the horizontal asymptote is y = 0.

xintercepts: To find the xintercepts, we set f(x) = 0 and solve for x. In this case, (1  x^2)/x = 0 when x = ±1.

yintercept: To find the yintercept, we substitute x = 0 into the function. In this case, f(0) = (1  0^2)/0 = undefined.
By considering these properties, we can graph the function f(x) = (1  x^2)/x accordingly.
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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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