How do you graph #f(x)= (x^2 +10x+ 24)/( x+6)#?
You can factorise the quadratic term and see where that gets you.
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To graph the function f(x) = (x^2 + 10x + 24)/(x + 6), follow these steps:

Determine the vertical asymptote: Set the denominator (x + 6) equal to zero and solve for x. The vertical asymptote occurs at x = 6.

Determine the horizontal asymptote: Compare the degrees of the numerator and denominator. Since the degree of the numerator (2) is greater than the degree of the denominator (1), there is no horizontal asymptote.

Find the xintercepts: Set the numerator (x^2 + 10x + 24) equal to zero and solve for x. The xintercepts occur when x = 4 and x = 6.

Find the yintercept: Substitute x = 0 into the function to find the yintercept. The yintercept is (0, 4).

Plot the points: Plot the vertical asymptote at x = 6, the xintercepts at x = 4 and x = 6, and the yintercept at (0, 4).

Determine the behavior of the graph: As x approaches negative infinity or positive infinity, the function approaches the vertical asymptote at x = 6.

Sketch the graph: Connect the plotted points and draw a smooth curve that approaches the vertical asymptote at x = 6.
This is the graph of f(x) = (x^2 + 10x + 24)/(x + 6).
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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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