Evaluate the function for the given values of $$ x $$. \[ f(x)=\left\{\begin{array}{cl} -3|x|+6 & \text { for } x \leq-2 \ 4 x+2 & \text { for }-2

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UpStudy AI · Accepted Answer

$$ \textbf{Part 1:} $$  
For $$ x = -3 $$, since $$ -3 \leq -2 $$, we use  
$$
f(x) = -3|x| + 6.
$$  
Thus,  
$$
f(-3) = -3|{-3}| + 6 = -3(3) + 6 = -9 + 6 = -3.
$$

---

$$ \textbf{Part 2:} $$  
For $$ x = 5 $$, since $$ 5 \geq 5 $$, we use  
$$
f(x) = 6.
$$  
Thus,  
$$
f(5) = 6.
$$

---

$$ \textbf{Part 3:} $$  
For $$ x = -2 $$, since $$ -2 \leq -2 $$, we use  
$$
f(x) = -3|x| + 6.
$$  
Thus,  
$$
f(-2) = -3|{-2}| + 6 = -3(2) + 6 = -6 + 6 = 0.
$$

---

$$ \textbf{Part 4:} $$  
For $$ x = 0 $$, since $$ -2 < 0 < 5 $$, we use  
$$
f(x) = 4x + 2.
$$  
Thus,  
$$
f(0) = 4(0) + 2 = 0 + 2 = 2.
$$

---

$$ \textbf{Part 5:} $$  
For $$ x = 6 $$, since $$ 6 \geq 5 $$, we use  
$$
f(x) = 6.
$$  
Thus,  
$$
f(6) = 6.
$$
$$ f(-3) = -3 $$, $$ f(5) = 6 $$, $$ f(-2) = 0 $$, $$ f(0) = 2 $$, $$ f(6) = 6 $$.

Evaluate the function for the given values of \( x \). \[ f(x)=\left\{\begin{array}{cl} -3|x|+6 & \text { for } x \leq-2 \\ 4 x+2 & \text { for }-2

Ask by Carlson Franklin. in the United States

Mar 10,2025

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Evaluate the function for the given values of \( x \). \[ f(x)=\left\{\begin{array}{cl} -3|x|+6 & \text { for } x \leq-2 \\ 4 x+2 & \text { for }-2 Ask by Carlson Franklin. in the United States Mar 10,2025