Consider the following. f(x) = x^2/x^2 + 36 (a) State the domain of the function

Question

Consider the following. f(x) = x^2/x^2 + 36 (a) State the domain of the function. all real numbers x all real numbers x except x = -6 all real numbers x except x = 36 all real numbers x except x = 6 all real numbers x except x = -6 and x = 6 (b) Identify a intercepts. (If an answer does not exist, enter DNE.) x-intercept (x, y) = () y-intercept (x, y) = ([0]) (c) Find any vertical and horizontal asymptotes. (Enter your answers as a comma-separated list of equations. If there are no y = 1, x = +6, - 6

Explanation / Answer

f(x)=x2/(x2+36)

Domain

The dnominator should not be zero

x2+36=0

x2=36

x=+-6i

Hence the domain is all real numbers

b.f(x)=x2/(x2+36)

Y intercept

To find the y intercept,we have to plug x=0

f(x)=0/0+36=0

Y intercept is (0,0)

X intercept

F(x)=0

x2/(x2+36)=0

x=0

X intercept=(0,0)

c. No vertical asymptote

Horizontal asymptote,y=1/1=1

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