g(x) square root of x^2-x-12

Question

sign chart needed

Answer 1

g(x) = sqr(x^2 - x - 12) = (x^2-x-12)^(1/2)

g(-6)= sqr30

g(-5)= sqr18

g(-4) = sqr8

g(-3)= 0

for x>-3, g(x) is imaginary

g(-2)= -sqr-6= isqr6

g(-1)= isqr10

g(0) = isqr12

with positive x, the g(x) values repeat in opposite order

for x<4, g(x) is imaginary

g(1) =isqr12

g(2) =isqr10

g(3) =-isqr6

g(4) =-0

g(5) =sqr8

g(6)=sqr18

g(7)=sqr30

g(x) = y = sqr(x^2 -x +12)

square both sides

y^2 = x^2 -x +12

y^2 -x^2 +x -12 = 0 is a hyperbola

with just the positive square root, y=+sqr(x^2-x+12) g(x) is half of a hyperbola