Question

P please help me ASAP

Answer 1

Rate of change means the slope.

Intervals considered x = 0 to x = 3.

At x = 0:

f(x) = 3/2x + 2

f(x) = (3/2)(0) + 2

f(x) = 2

At x = 3:

f(x) = 3/2x + 2

f(x) = (3/2)(3) + 2

f(x) = 4.5 + 2

f(x) = 6.5

`\begin{gathered} \text{Rate of Change = }(f(x)_3-f(x)_0)/(x_3-x_0) \\ \text{Rate of Change = }(6.5-2)/(3-0)=(4.5)/(3)=(3)/(2) \end{gathered}`

The average rate of change for f(x) is 3/2.

Let's now solve for the average rate of change of g(x).

`\begin{gathered} \text{Rate of Change = }(g(x)_3-g(x)_0)/(x_3-x_0) \\ \text{Rate of Change = }(-10-(-4))/(3-0)=(-6)/(3)=-2 \end{gathered}`

The average rate of change for g(x) is -2.

Comparing the two averages, f(x) is greater than g(x).

The answer is Option 1.