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

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

The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.

put like terms together.orremember that the 45 becomes negative when moved to the other side.orthe minuses cancel out.