(e) Find the net change in $$ h $$ between $$ x=-3 $$ and $$ x=3 $$. -3

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UpStudy AI · Accepted Answer

To determine the **net change** in the function $$ h(x) $$ between $$ x = -3 $$ and $$ x = 3 $$, you can use the following formula:

$$
\text{Net Change} = h(3) - h(-3)
$$

Here's a step-by-step guide to finding the net change:

1. **Evaluate $$ h(3) $$:**
   - Substitute $$ x = 3 $$ into the function $$ h(x) $$ to find $$ h(3) $$.

2. **Evaluate $$ h(-3) $$:**
   - Substitute $$ x = -3 $$ into the function $$ h(x) $$ to find $$ h(-3) $$.

3. **Calculate the Net Change:**
   - Subtract the value of $$ h(-3) $$ from $$ h(3) $$:
     $$
     \text{Net Change} = h(3) - h(-3)
     $$

**Example:**

Suppose you have the function $$ h(x) = 2x + 1 $$. Let's find the net change between $$ x = -3 $$ and $$ x = 3 $$.

1. **Find $$ h(3) $$:**
   $$
   h(3) = 2(3) + 1 = 6 + 1 = 7
   $$

2. **Find $$ h(-3) $$:**
   $$
   h(-3) = 2(-3) + 1 = -6 + 1 = -5
   $$

3. **Calculate the Net Change:**
   $$
   \text{Net Change} = h(3) - h(-3) = 7 - (-5) = 7 + 5 = 12
   $$

In this example, the net change in $$ h $$ between $$ x = -3 $$ and $$ x = 3 $$ is **12**.

---

**Regarding Your Answer (-3):**

If you've determined that the net change is **-3**, ensure that you've correctly evaluated $$ h(3) $$ and $$ h(-3) $$ based on the specific function $$ h(x) $$ provided in your problem. Here's how you can verify:

1. **Double-check the Function:** Ensure that you're using the correct expression for $$ h(x) $$.
2. **Re-evaluate $$ h(3) $$ and $$ h(-3) $$:** Substitute the values carefully to avoid calculation errors.
3. **Subtract Properly:** Remember that net change is $$ h(3) - h(-3) $$, not the other way around.

If, after following these steps, you still arrive at **-3**, then your answer is correct based on the function provided.

If you need further assistance, feel free to provide the specific function $$ h(x) $$, and I can help you work through the calculations!
To find the net change in $$ h $$ between $$ x = -3 $$ and $$ x = 3 $$, subtract $$ h(-3) $$ from $$ h(3) $$.

(e) Find the net change in \( h \) between \( x=-3 \) and \( x=3 \). -3

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