Asymptotes and zeros of

Question

f(x)=2x^2-18/ x^2-16?

 

Please help me out; thanks

 

Answer 1

The rational function

Change f(x) to y.

• Find asymptotes of rational function.

Vertical asymptotes are found  by solving denominator = 0

Vetical asymptotes are x = 4 and x =  - 4.

To find horizontal asymptote.

Degree of the numarator = 2 and the degree of denominator = 2.

If the degree of the numerator is equal to the degree of the denominator, then horizontal asymptote is

y = [leading coefficient of numarator]/[leading coefficient of numarator].

In this case y = 2/1

y = 2 is the horizontal asymptote.

• To find zeros of rational function.

 x intercept and y intercepts are zeros of the function.

To find x  intercept substitute y  = 0 in

x  intercepts are (3, 0) and (- 3, 0)

To find y  intercepts substitute x  = 0 in

y  = 9/8

y  = 1.125

y  intercept is (0,1.125).

Zeros of the function (0, 1.125), (3, 0) and (- 3, 0).