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
