Which function has a range of {y|y ≤ 5}?

f(x) = (x – 4)2 + 5
f(x) = –(x – 4)2 + 5
f(x) = (x – 5)2 + 4
f(x) = –(x – 5)2 + 4

The correct option is 2.

Step-by-step explanation:

The range of a parabola is {y|y ≤ 5}.

It means the maximum value of the function is 5. It is possible if the vertex of a downward parabola is in the form of (h,5).

The vertex form of a parabola is

Where, (h,k) is vertex and a is a constant.

If a<0, then f(x) is a down ward parabola and if a>0, then f(x) is an upward parabola.

In option 1,

It is an upward parabola with vertex (4,5), therefore the range of the function is {y|y ≥ 5}. Option 1 is incorrect.

In option 2,

It is a downward parabola with vertex (4,5), therefore the range of the function is {y|y ≤ 5}. Option 2 is correct.

In option 3,

It is an upward parabola with vertex (5,4), therefore the range of the function is {y|y ≥ 4}. Option 3 is incorrect.

In option 4,

It is a downward parabola with vertex (5,4), therefore the range of the function is {y|y ≤ 4}. Option 4 is incorrect.