Question

Evaluate each piecewise function at the given values of

the independent variable.
+ 5
(x + 5 if x 2-5
8(x) =
1-(x + 5) if x<-5
a. 8(0)
b. 8(-6)
c. 8(-5)

Answer 1

To evaluate the piecewise function, use the appropriate function based on whether x is greater than, less than, or equal to -5. For �(0), �(-6), and �(-5), the results are 25, 2, and 0, respectively.

Step-by-step explanation:

To evaluate the piecewise function at the given values of the independent variable:

�(x) = �(x + 5) if x ≥ -5
�(x) = 1 - (x + 5) if x < -5

1. For �(0), since 0 is greater than -5, we use the first function: �(0) = 5(0 + 5) = 5×5 = 25.
2. For �(-6), since -6 is less than -5, we use the second function: �(-6) = 1 - (-6 + 5) = 1 - (-1) = 2.
3. For �(-5), since -5 is equal to -5, we typically use the function that is defined at the boundary, which is the first function: �(-5) = 5(-5 + 5) = 5×0 = 0.

It is important to choose the correct part of the piecewise function to use based on the value of x in relation to the condition for each piece.