# How do you find intercepts, extrema, points of inflections, asymptotes and graph #f(x)=(2x^2-5x+5)/(x-2)#?

Two asymptotes; two

Then differentiate this function, applying the chain rule and product rules where necessary.

The product rule isn't really necessary as it's pretty clear you will end up with:

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To find intercepts, set ( f(x) ) equal to zero and solve for ( x ). For extrema, find the critical points by setting the derivative of ( f(x) ) equal to zero and solve for ( x ). Points of inflection occur where the second derivative of ( f(x) ) changes sign or is zero. To find them, find the second derivative and solve for ( x ). To find asymptotes, determine the vertical asymptotes by finding where the denominator of ( f(x) ) is zero (except where the numerator is also zero, which would be holes in the graph). Horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. To graph the function, use the intercepts, extrema, points of inflection, asymptotes, and any other relevant information.

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When evaluating a one-sided 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 one-sided 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 one-sided 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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