Question

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

Answer 1

Since the range has less than sign, this means that the parabola is facing downwards and it means that a is negative.
Range is given by {y|y ≤ k}, and the vertex for of a quadratic equation is given by$f(x)=a (x-h)^{2} +k$
Since the range is {y|y ≤ 5}, this means that k = 5 and since a is negative
The correct function is $f(x)=-(x-4)^{2}+5$

Answer 2

The function that has a range of {y|y ≤ 5} is (b) f(x) = -(x - 4)² + 5

How to determine the function with the range?

The given options are quadratic functions

Quadratic functions are represented using

f(x) = a(x - h)² + k

Where:

k is the minimum or the maximum output value of the function.

If a is negative, then k is maximum

By considering option (b), we have:

a = -1 and k = 5

This means that the maximum of f(x) = -(x - 4)² + 5 is 5

Hence, the function that has a range of {y|y ≤ 5} is (b) f(x) = -(x - 4)² + 5

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