Question

The graph of the function g(x) is given for #1 - 5.

1. Which of the following is the given function's
average rate of change on the interval
-3≤x≤-2?
A-2
ОВ
D c
1222
OD 2
1|2
2. Which of the following is the given function's
average rate of change on the interval
-2 ≤x≤ 1?
□A-2
OB-3
OC
OD 2
3. Based on the graph of g(x), on which intervals
are the function's values positive? Select all that
apply.
□A -∞0 < x < -3
0 B -3 < x < -1
□C -1 < x < 2
□D 2

Answer 1

1. The average rate of change on the interval -3<=x<=-2 is 2.

(Using the coordinates (-3,-2) and (-2,0), the average rate of change is (0-(-2))/(2-(-3)) = 2)

2. The average rate of change on the interval -2<=x<=-1 is -1/2.

(Using the coordinates (-2,0) and (-1,4), the average rate of change is (4-0)/(-1-(-2)) = -1/2)

3. Based on the graph of g(x), the function's values are positive on intervals:

b. -3<x<-1

c. -1<x<2

d. 2<x<\infinity

4. Based on the graph of g(x), the function's values are negative on intervals:

a. -\infinity<x<-3

5. The zeroes of the function are at x=-3, x=-1, and x=2 where y=0.

**1. Average Rate of Change on the Interval
`\(-3 \leq x \leq -2\)`:**

The correct average rate of change is indeed 2, calculated using the coordinates (-3, -2) and (-2, 0). The formula
`\((g(-2) - g(-3))/((-2) - (-3))\)` yields
`\((0 - (-2))/(1) = 2\).`

**2. Average Rate of Change on the Interval
`\(-2 \leq x \leq -1\)`:**

The accurate average rate of change is
`\(-(1)/(2)\)`, determined using the coordinates (-2, 0) and (-1, 4). The formula
`\((g(-1) - g(-2))/((-1) - (-2))\) results in \((4-0)/(-1-(-2)) = -(1)/(2)\).`

**3. Intervals where Function Values are Positive:**

The graph illustrates positive values in intervals b.
`\(-3 < x < -1\), c. \(-1 < x < 2\), and d. \(2 < x < \infty\).`

**4. Intervals where Function Values are Negative:**

The function's values are negative only in interval a.
`\(-\infty < x < -3\).`

**5. Zeroes of the Function:**

The zeroes of the function, where y = 0, are at x = -3, x = -1, and x = 2. These points signify where the graph intersects the x-axis, indicating locations where the function evaluates to zero.