Question

Find each function value for part 1, 3 and 5 with the given function

Answer 1

Answer:

1. -25

3. 15

5. -5/4

Explanation:

Considering the given functions for a(x)

1. To solve for a(8), we'll have to use the third function since we're given that x > 1 in the 3rd function and we know that 8 is greater than 1.

So we'll have;

$\begin{gathered} a(x)=-4x+7_{} \\ a(8)=-4(8)+7 \\ a(8)=-32+7 \\ a(8)=-25 \end{gathered}$

3. To solve for a(-7), we'll use the 1st function because -7 is less than -6 and the condition is x <= -6;

$\begin{gathered} a(x)=|x-8| \\ a(-7)=|-7-8| \\ a(-7)=|-15| \\ a(-7)=15 \end{gathered}$

5. a(-1/2)

In this case, we'll use the 2nd function is -1/2 lies between -6 and 1.

So, we'll have;

$\begin{gathered} a(x)=2x-x^2 \\ a(-\frac{1}{2})=2(-\frac{1}{2})-(-\frac{1}{2})^2 \\ =-1-(\frac{1}{4}) \\ =\frac{-4-1}{4} \\ =-\frac{5}{4} \end{gathered}$