A function is given. $$ g(x)=8-\frac{1}{2} x ; x=-2, x=1 $$ (a) Determine the net change between the given values of the variable. (b) Determine the average rate of change between the given values of the variable. (b)

Question

UpStudy AI · Accepted Answer

Let's analyze the function $$ g(x) = 8 - \frac{1}{2}x $$ over the interval where $$ x $$ changes from $$-2$$ to $$1$$.

### (a) Net Change

**Net change** refers to the difference in the function's values between the two points.

1. **Calculate $$ g(-2) $$:**
   $$
   g(-2) = 8 - \frac{1}{2}(-2) = 8 + 1 = 9
   $$

2. **Calculate $$ g(1) $$:**
   $$
   g(1) = 8 - \frac{1}{2}(1) = 8 - 0.5 = 7.5
   $$

3. **Determine the net change:**
   $$
   \text{Net Change} = g(1) - g(-2) = 7.5 - 9 = -1.5
   $$
   
   **Interpretation:** The function decreases by $$1.5$$ units as $$x$$ increases from $$-2$$ to $$1$$.

### (b) Average Rate of Change

The **average rate of change** measures how much the function changes per unit increase in $$x$$ over the interval.

1. **Use the formula for average rate of change:**
   $$
   \text{Average Rate of Change} = \frac{g(1) - g(-2)}{1 - (-2)} = \frac{-1.5}{3} = -0.5
   $$
   
   **Interpretation:** On average, the function decreases by $$0.5$$ units for each unit increase in $$x$$ between $$-2$$ and $$1$$.

---

**Summary:**
- **Net Change:** $$-1.5$$
- **Average Rate of Change:** $$-0.5$$ per unit of $$x$$
The function decreases by 1.5 units from $$ x = -2 $$ to $$ x = 1 $$. On average, it decreases by 0.5 units per unit increase in $$ x $$ over this interval.

A function is given. \( g(x)=8-\frac{1}{2} x ; x=-2, x=1 \) (a) Determine the net change between the given values of the variable. (b) Determine the average rate of change between the given values of the variable. (b)

Real Tutor Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Calculus Questions