Questions: HW: Sections 2.1 - 2.7 Assignment DETAILS MY NOTES SCOLALG7 2.4.011.MI. function is given. f(x)=5x-2; x=2, x=3 (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.

Solution Steps

To solve the given problem, we need to evaluate the function at the specified values of \( x \) and then use these evaluations to find the net change and the average rate of change.

(a) Net Change: Calculate the function values at \( x = 2 \) and \( x = 3 \). The net change is the difference between these two function values.

(b) Average Rate of Change: Use the formula for the average rate of change, which is the difference in function values divided by the difference in \( x \) values.

We evaluate the function \( f(x) = 5x - 2 \) at the given points \( x_1 = 2 \) and \( x_2 = 3 \): \[ f(2) = 5(2) - 2 = 10 - 2 = 8 \] \[ f(3) = 5(3) - 2 = 15 - 2 = 13 \]

The net change between the function values at \( x_1 \) and \( x_2 \) is calculated as follows: \[ \text{Net Change} = f(3) - f(2) = 13 - 8 = 5 \]

The average rate of change between the given values of \( x \) is computed using the formula: \[ \text{Average Rate of Change} = \frac{f(3) - f(2)}{3 - 2} = \frac{13 - 8}{1} = 5.0 \]

Final Answer