Question

What is the range of the function f(x) = -|x - 4| + 5?

Answer 1

Option 1st is correct.

Explanation:

We have been given the function:
`f(x)=-|x-4|+5`

So, range of the function is the values that y will take.

Absolute function
`-|x-4|` will always gives negative value because value inside the modulus function will be positive

But we have minus sign outside it will always give negative value.

So, Range will be:
`(-\infty,5]`

Any value in first parent function that is modulus function will always give value less than or equal to 5.

Therefore, close bracket with 5.

Therefore, Option 1st is correct.

Answer 2

The range of the absolute value function is [0, ∞). Subtracting that from 5 gives
(-∞, 5]