How do you graph #f(x)= (2x^2+7x15) / (x+5)# and identify all the asymptotes and domain?
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To graph the function f(x) = (2x^2 + 7x  15) / (x + 5) and identify the asymptotes and domain, follow these steps:

Determine the domain:
 The function is defined for all real numbers except when the denominator (x + 5) equals zero.
 Therefore, the domain of f(x) is all real numbers except x = 5.

Identify vertical asymptotes:
 Vertical asymptotes occur when the denominator equals zero.
 Set x + 5 = 0 and solve for x.
 x = 5 is the vertical asymptote.

Determine horizontal asymptotes:
 To find horizontal asymptotes, compare the degrees of the numerator and denominator.
 If the degree of the numerator is less than the degree of the denominator, there is a horizontal asymptote at 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.

Graph the function:
 Plot points on the graph by substituting different xvalues into the function.
 Use the obtained points to draw a smooth curve that represents the function.
 Take note of the vertical asymptote at x = 5.
In summary, the graph of f(x) = (2x^2 + 7x  15) / (x + 5) has a vertical asymptote at x = 5. The domain of the function is all real numbers except x = 5. The presence of a horizontal asymptote depends on the degrees of the numerator and denominator.
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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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