State the x and yintercepts and the vertical and horizontal

State the x- and y-intercepts and the vertical and horizontal asymptotes.

Solution:

let this graph is function of f(x)

for x intercept , when f(x) = 0

and thus it is zeros of numerator

therefore we can see that f(x) touches x axis

x = -1 and x = 1

terms contained in numerator (x-1) and (x+1)

Now

Vertical asymtotes

f(x) tends to infinity

we can see that it is at x = -3 and x=3

and it is zeros of denominator

denominator contained of f(x)

(x-3) and (x+3)

and we can see that Horizontal aysmptotes is at y = 1

thus leading coffiecient of numerator and denominator is same

thus f(x) = (x-1)(x-1)/(x-3) (x+3)

plug x = 0

for y intercept

f(x) = 1/(9) = 1/9

is y intercept

Answer