Questions: Evaluate the function for the given values of (x). [ f(x)=leftbeginarraycl -3 x+7 text for x<-1 x^2+2 text for -1 leq x<5 6 text for x geq 5 endarrayright. ] Part 1 of 5 [ f(0)= ] Part 2 of 5 [ f(-2)= ]

Evaluate the function for the given values of (x).
[
f(x)=leftbeginarraycl
-3 x+7 text for x<-1
x^2+2 text for -1 leq x<5
6 text for x geq 5
endarrayright.
]

Part 1 of 5
[
f(0)=
]

Part 2 of 5
[
f(-2)=
]

Transcript text: Evaluate the function for the given values of $x$. \[ f(x)=\left\{\begin{array}{cl} -3 x+7 & \text { for } x<-1 \\ x^{2}+2 & \text { for }-1 \leq x<5 \\ 6 & \text { for } x \geq 5 \end{array}\right. \] Part 1 of 5 \[ f(0)= \] Part 2 of 5 \[ f(-2)= \]

Solution

Solution Steps

Step 1: Evaluate $f(0)$

To evaluate $f(0)$, we first determine which piece of the piecewise function applies to $x = 0$. Since $-1 \leq 0 < 5$, we use the second piece of the function: \[ f(x) = x^{2} + 2 \] Substitute $x = 0$ into the equation: \[ f(0) = (0)^{2} + 2 = 0 + 2 = 2 \]

Step 2: Evaluate $f(-2)$

To evaluate $f(-2)$, we determine which piece of the piecewise function applies to $x = -2$. Since $-2 < -1$, we use the first piece of the function: \[ f(x) = -3x + 7 \] Substitute $x = -2$ into the equation: \[ f(-2) = -3(-2) + 7 = 6 + 7 = 13 \]

Final Answer

\[ \boxed{f(0) = 2} \] \[ \boxed{f(-2) = 13} \]

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