Answer:
f(-4) = 1
f(0) = 1
f(1) = - [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
1 if x ≤ -2
f(x) = -(x - 1)² + 2 if -2 < x < 1
- [tex]\frac{1}{2}[/tex] x - 1 if x ≥ 1
To find f(-4)
∵ -4 < -2
- That means we will use f(x) = 1 because value of x in this
part is ≤ -2
∴ f(x) = 1
- Substitute x by -4, and remember f(x) = 1 is a constant function
which means the value of y for any value of x is 1
∴ f(-4) = 1
To find f(0)
∵ -2 < 0 < 1
- That means we will use f(x) = -(x - 1)² + 2 because value of x in this
part is between -2 and 1
∴ f(x) = -(x - 1)² + 2
- Substitute x by 0
∴ f(0) = -(0 - 1)² + 2
∴ f(0) = -(-1)² + 2
∴ f(0) = -1 + 2
∴ f(0) = 1
To find f(1)
∵ 1 ≥ 1
- That means we will use f(x) = - [tex]\frac{1}{2}[/tex] x - 1 because value of x in this
part ≥ 1
∴ f(x) = - [tex]\frac{1}{2}[/tex] x - 1
- Substitute x by 1
∴ f(1) = - [tex]\frac{1}{2}[/tex] (1) - 1
∴ f(1) = - [tex]\frac{1}{2}[/tex] - 1
∴ f(1) = - [tex]\frac{3}{2}[/tex]
