Question

Determine which function has a range of {y∣y≤3}. f f(x)=-2x−3 g f(x)=-2|x+3|−3 h f(x)=-2(x−4)2+3 j f(x)=-2x3+3x2+x−1

Answer 1

See the attached figure.
f(x)=-2x−3 ⇒⇒ black graph ⇒⇒ range = R


g(x)=-2|x+3|−3 ⇒⇒ red graph ⇒⇒ range = {y∣y ≤ -3}


h(x)=-2(x−4)²+3 ⇒⇒ blue graph ⇒⇒ range = {y∣y ≤ 3}


j(x)=-2x³+3x²+x−1 ⇒⇒ green graph ⇒⇒ range = R


∴ The function which has a range of {y∣y ≤ 3} is h(x)=-2(x−4)²+3

   Which is the third choice