For the piecewise function, find the values $$ g(-4), g(4) $$, and $$ g(7) $$. $$ g(x)=\left\{\begin{array}{l}x+9, ext { for } x \leq 4 \ 8-x, ext { for } x4\end{array} ight. $$ $$ g(-4)=\square $$

Question

For the piecewise function, find the values $$ g(-4), g(4) $$, and $$ g(7) $$. $$ g(x)=\left\{\begin{array}{l}x+9, 	ext { for } x \leq 4 \ 8-x, 	ext { for } x>4\end{array}ight. $$ $$ g(-4)=\square $$

UpStudy AI · Accepted Answer

To find the values of the piecewise function $$ g(x) $$ at specific points, we'll evaluate each case based on the given conditions.

The piecewise function is defined as:
$$
g(x) = \begin{cases}
x + 9 & \text{for } x \leq 4 \
8 - x & \text{for } x > 4
\end{cases}
$$

Let's evaluate $$ g(-4) $$, $$ g(4) $$, and $$ g(7) $$ one by one.

---

### 1. Finding $$ g(-4) $$

**Step 1:** Determine which piece of the function to use by checking the condition for $$ x = -4 $$.

- Since $$ -4 \leq 4 $$, we use the first case:
  $$
  g(-4) = (-4) + 9
  $$

**Step 2:** Perform the calculation:
$$
g(-4) = -4 + 9 = 5
$$

**Answer:**
$$
g(-4) = 5
$$

---

### 2. Finding $$ g(4) $$

**Step 1:** Determine which piece of the function to use by checking the condition for $$ x = 4 $$.

- Since $$ 4 \leq 4 $$, we use the first case:
  $$
  g(4) = 4 + 9
  $$

**Step 2:** Perform the calculation:
$$
g(4) = 4 + 9 = 13
$$

**Answer:**
$$
g(4) = 13
$$

---

### 3. Finding $$ g(7) $$

**Step 1:** Determine which piece of the function to use by checking the condition for $$ x = 7 $$.

- Since $$ 7 > 4 $$, we use the second case:
  $$
  g(7) = 8 - 7
  $$

**Step 2:** Perform the calculation:
$$
g(7) = 8 - 7 = 1
$$

**Answer:**
$$
g(7) = 1
$$

---

### Summary of Results

$$
\begin{align*}
g(-4) &= 5 \
g(4) &= 13 \
g(7) &= 1
\end{align*}
$$
$$ g(-4) = 5 $$, $$ g(4) = 13 $$, and $$ g(7) = 1 $$.

For the piecewise function, find the values \( g(-4), g(4) \), and \( g(7) \). \( g(x)=\left\{\begin{array}{l}x+9, \text { for } x \leq 4 \\ 8-x, \text { for } x>4\end{array}\right. \) \( g(-4)=\square \)

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