Question

Given g(x)=-4x+8, identify the domain, range, and x-intercept of the function.

please give an explanation if you can. thanks :)

Answer 1

1st option: Domain: -∞ < x < ∞. Range: -∞ < y < ∞. x-intercept: (2, 0)

Explanation:

g(x)=-4x+8

x is all real numbers since there are no real restrictions, so the domain is:

Domain: -∞ < x < ∞

The domain can't equal ∞ as ∞ is not a real number.

g(x) is also all real numbers, so the range is:

Range: -∞ < y < ∞

The x-intercept is calculated when g(x)=0:
0=-4x+8 ==> solve for x

4x=8 ==> add 4x on both sides to remove negative x and isolate x

x=2 ==> divide both sides by 2 to isolate x

Hence, x=2 when g(x)=0, so the x-intercept is:

x-intercept: (2, 0)

1st option: Domain: -∞ < x < ∞. Range: -∞ < y < ∞. x-intercept: (2, 0)