$$ f(x)=\left\{\begin{array}{cc}5 & ext { if } x \leq-3 \ -x+2 & ext { if }-3

Question

$$ f(x)=\left\{\begin{array}{cc}5 & 	ext { if } x \leq-3 \ -x+2 & 	ext { if }-3

UpStudy AI · Accepted Answer

The function $$ f(x) $$ is defined piecewise, meaning it has different expressions based on the value of $$ x $$. Let's break down the function into its three cases:

1. **Case 1:** If $$ x \leq -3 $$, then $$ f(x) = 5 $$.
2. **Case 2:** If $$ -3 < x < 3 $$, then $$ f(x) = -x + 2 $$.
3. **Case 3:** If $$ x \geq 3 $$, then $$ f(x) = 2 $$.

Now, let's analyze the function further. We can evaluate $$ f(x) $$ for specific values of $$ x $$ to understand its behavior.

### Step 1: Evaluate $$ f(x) $$ at specific points

- **For $$ x = -4 $$:**
  - Since $$ -4 \leq -3 $$, we use Case 1:
  $$
  f(-4) = 5
  $$

- **For $$ x = -2 $$:**
  - Since $$ -3 < -2 < 3 $$, we use Case 2:
  $$
  f(-2) = -(-2) + 2 = 2 + 2 = 4
  $$

- **For $$ x = 0 $$:**
  - Since $$ -3 < 0 < 3 $$, we use Case 2:
  $$
  f(0) = -0 + 2 = 2
  $$

- **For $$ x = 3 $$:**
  - Since $$ 3 \geq 3 $$, we use Case 3:
  $$
  f(3) = 2
  $$

- **For $$ x = 4 $$:**
  - Since $$ 4 \geq 3 $$, we use Case 3:
  $$
  f(4) = 2
  $$

### Summary of Evaluations
- $$ f(-4) = 5 $$
- $$ f(-2) = 4 $$
- $$ f(0) = 2 $$
- $$ f(3) = 2 $$
- $$ f(4) = 2 $$

### Step 2: Analyze the function's behavior
- For $$ x \leq -3 $$, the function is constant at 5.
- For $$ -3 < x < 3 $$, the function decreases linearly from $$ f(-3) = 5 $$ to $$ f(3) = 2 $$.
- For $$ x \geq 3 $$, the function is constant at 2.

### Conclusion
The piecewise function $$ f(x) $$ has a constant value of 5 for $$ x \leq -3 $$, decreases linearly between $$ -3 $$ and $$ 3 $$, and then becomes constant at 2 for $$ x \geq 3 $$. If you have any specific questions or need further analysis, feel free to ask!
The function $$ f(x) $$ is defined as: - $$ f(x) = 5 $$ when $$ x \leq -3 $$ - $$ f(x) = -x + 2 $$ when $$ -3 < x < 3 $$ - $$ f(x) = 2 $$ when $$ x \geq 3 $$ For example: - $$ f(-4) = 5 $$ - $$ f(-2) = 4 $$ - $$ f(0) = 2 $$ - $$ f(3) = 2 $$ - $$ f(4) = 2 $$ The function is constant at 5 for $$ x \leq -3 $$, decreases linearly between $$ -3 $$ and $$ 3 $$, and remains constant at 2 for $$ x \geq 3 $$.

\( f(x)=\left\{\begin{array}{cc}5 & \text { if } x \leq-3 \\ -x+2 & \text { if }-3

Ask by Potter Estrada. in the United States

Mar 06,2025

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\( f(x)=\left\{\begin{array}{cc}5 & \text { if } x \leq-3 \\ -x+2 & \text { if }-3 Ask by Potter Estrada. in the United States Mar 06,2025