Let's analyze the given piecewise function and calculate the required values step-by-step for each specified input.
The piecewise function is defined as:
[tex]\[
f(x)=\left\{\begin{array}{ll}
4x - 7 & \text{if } x < 0 \\
4x - 14 & \text{if } x \geq 0
\end{array}\right.
\][/tex]
Step 1: Calculate [tex]\( f(-1) \)[/tex]
Given [tex]\( x = -1 \)[/tex], which is less than 0, we use the first part of the piecewise function:
[tex]\[ f(x) = 4x - 7 \][/tex]
Substituting [tex]\( x = -1 \)[/tex]:
[tex]\[
f(-1) = 4(-1) - 7
\][/tex]
[tex]\[
f(-1) = -4 - 7
\][/tex]
[tex]\[
f(-1) = -11
\][/tex]
Step 2: Calculate [tex]\( f(0) \)[/tex]
Given [tex]\( x = 0 \)[/tex], which is equal to 0, we use the second part of the piecewise function:
[tex]\[ f(x) = 4x - 14 \][/tex]
Substituting [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = 4(0) - 14
\][/tex]
[tex]\[
f(0) = 0 - 14
\][/tex]
[tex]\[
f(0) = -14
\][/tex]
Step 3: Calculate [tex]\( f(2) \)[/tex]
Given [tex]\( x = 2 \)[/tex], which is greater than 0, we use the second part of the piecewise function:
[tex]\[ f(x) = 4x - 14 \][/tex]
Substituting [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = 4(2) - 14
\][/tex]
[tex]\[
f(2) = 8 - 14
\][/tex]
[tex]\[
f(2) = -6
\][/tex]
Summary of Results:
- [tex]\( f(-1) = -11 \)[/tex]
- [tex]\( f(0) = -14 \)[/tex]
- [tex]\( f(2) = -6 \)[/tex]
