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

has a range {y|y ≤ 5}

Step-by-step explanation:

We have been given the range as {y|y ≤ 5} and we have to find the function.

Range is the set of y values for which the function is defined.

All the given options are the equations of parabola. And we know that the vertex of a parabola is max/min point.

Now, the range is all real y values less than equal to 5. Hence, the y coordinate of the parabola is 5 and must be a downward parabola.

We have to check which parabola is downward parabola and having y coordinate of vertex as 5.

The vertex form of a parabola is given by

From the given options, only options (b) and (d) have negative value of 'a'. and the vertex of option (b) is (4,5).

Therefore, has a range {y|y ≤ 5}