What is the range and domain, x and y intercepts, symmetry and asymptote of this given equation, f(x) = 2x^2 - 8 / x-1

Answer 1

all polynomials have a domain of (-∞,∞)

Rational functions do too, except where the denominator is zero. So,
f(x) has a domain of (-∞,1)U(1,∞)

Near x=1, 2x^2-8 is near -6.
So, for
x<1 y->∞
x>1 y->-∞
So, f(x) has a range of (-∞,∞)

2x^2-8 = 2(x-2)(x+2)
Since a fraction is zero when the numerator is zero, y=0 at x=±2

f(0) = 8

As or symmetry, this is a rotated hyperbola, rotated through an angle of -13.28°