Determine whether the rational function has symmetry with re

Determine whether the rational function has symmetry with respect to the origin, symmetry with respect to the y-axis, or neither. f(x) = (5x - 15)(x - 6)/x^2 + 18x - 19

Solution

given f(x) = (5x-15) (x-6) / (x^2 +18x-19)

so y =(5x-15) (x-6) / (x^2 +18x-19)

to find the symetry about y axis plug y =-y

so -y = (5x-15) (x-6) / (x^2 +18x-19)

so y = - (5x-15) (x-6) / (x^2 +18x-19)

this y value is different from the given function so

it is not symetric about y-axis.

to check symetric about origin plug(-x,-y) in the place of(x,y)

-y = (-5x-15)(-x-6) /( (-x)^2 +19(-x) -18)

-y = (5x+15)(x+6) /(x^2 -19x-18)

so y = - (5x+15) (x+6) /(x^2-19x -18)

so this y value is different from the given function so this not symetric about origin also.

Answer: Neither