Question

for the piecewise linear function, find (a) ( f(-4) ), (b) ( f(-1) ), (c) ( f(0) ), (d) ( f(2) ), and (e) ( f(4) ).
f(x) = \begin{cases} 2x & \text{if } x leq -1 \\ x - 1 & \text{if } x > -1 end{cases}
(a) ( f(-4) = -8 )
(b) ( f(-1) = -2 )
(c) ( f(0) = -1 )
(d) ( f(2) = square )

Explanation:

Step1: Determine the applicable piece of the function

Since \( 2 > -1 \), we use the second piece of the piecewise function, which is \( f(x)=x - 1 \) when \( x > -1 \).

Step2: Substitute \( x = 2 \) into the function

Substitute \( x = 2 \) into \( f(x)=x - 1 \):
\( f(2)=2 - 1 \)

Step3: Calculate the result

\( 2 - 1 = 1 \)

Answer:

\( f(2)=\boxed{1} \)