Answer:
Explanation:
Explaining the Basic Concept:
This is a piecewise function, which means that it is made up of several different functions which all have different domains
In this question, we have 3 'pieces' in our piecewise function
the domain of each piece is:
1. x < -1
2. -1 ≤ x ≤ 2
3. x > 2
we will use the function related with the respective domain
Finding the values of the function:
h(-4)
Here, our input value is -4
we notice that -4 is in part of the first domain
therefore, -4 is in the domain of the first function
So, we will use the first function
h(x) = -(x/4) + 2 (for x < -1)
replacing x with -4
h(-4) = -(-4/4) + 2
h(-4) = 1 + 2
h(-4) = 3
h(1):
Here, our input value is 1
we notice that 1 is a part of the second domain
Hence, 1 is in the domain of the second function
So, we will use the second function
h(x) = -(x-1)² + 2 (for -1 ≤ x ≤ 2)
replacing x with 1
h(1) = -(1-1)² + 2
h(1) = -(0)² + 2
h(1) = 2
h(2):
Here, out input value is 2
We notice that 2 is a part of the second domain
Hence, 2 is a part of the domain of the second function
So, we will use the second function
h(x) = -(x-1)² + 2 (for -1 ≤ x ≤ 2)
replacing x with 2
h(2) = -(2-1)² + 2
h(2) = -(1)² + 2
h(2) = - 1 + 2
h(2) = 1
Therefore:
h(-4) = 3
h(1) = 2
h(2) = 1