Consider the function below. (If you need to use -infinity or infinity, enter -I

Question

Consider the function below. (If you need to use -infinity or infinity, enter -INFINITY or INFINITY.) f(x) = x^2/x^2 - 16 Find the vertical and horizontal asymptotes. x = (smaller value) x = (larger value) y = Find the intervals where the function is increasing. (Enter the interval that contains smaller numbers first.) Find the intervals where the function is decreasing, (Enter the interval that contains smaller numbers first.) Find the local maximum value. Find the intervals where the function is concave up. (Enter the interval that contains smaller numbers first.) Find the Interval where the function is concave down.

Explanation / Answer

To find vertical asymptote, we need to make denominator =0

So x2 -16 =0

=> x2 =16

=> x = 4 or x=-4

Vertical asymptotes are

x= 4(greater value) and x= -4(smaller value)

Since the coefficient of x2 in the numerator = the coefficient of x2 in the denominator =1,

horizontal asymptote = y = 1/1 =1 = ratio of the coefficient of x2 in the numerator and denominator

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