select the correct answer.\nconsider function g.\ng(z)=\\frac{5}{z - 1}+2\nwhat is the average rate of…

select the correct answer.\nconsider function g.\ng(z)=\\frac{5}{z - 1}+2\nwhat is the average rate of change of function g over the interval -4, 3?\na. \\frac{1}{2}\nb. -\\frac{1}{2}\nc. 2\nd. -\\frac{7}{2}

select the correct answer.\nconsider function g.\ng(z)=\\frac{5}{z - 1}+2\nwhat is the average rate of change of function g over the interval -4, 3?\na. \\frac{1}{2}\nb. -\\frac{1}{2}\nc. 2\nd. -\\frac{7}{2}

Answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = g(x)) over the interval ([a,b]) is (\frac{g(b)-g(a)}{b - a}). Here, (a=-4) and (b = 3).

Step2: Calculate (g(-4))

Substitute (x=-4) into (g(x)=\frac{5}{x - 1}+2). [ \begin{align*} g(-4)&=\frac{5}{-4-1}+2\ &=\frac{5}{-5}+2\ &=-1 + 2\ &=1 \end{align*} ]

Step3: Calculate (g(3))

Substitute (x = 3) into (g(x)=\frac{5}{x - 1}+2). [ \begin{align*} g(3)&=\frac{5}{3-1}+2\ &=\frac{5}{2}+2\ &=\frac{5 + 4}{2}\ &=\frac{9}{2} \end{align*} ]

Step4: Calculate the average rate of change

Use the formula (\frac{g(b)-g(a)}{b - a}), with (a=-4), (b = 3), (g(-4)=1), and (g(3)=\frac{9}{2}). [ \begin{align*} \frac{g(3)-g(-4)}{3-(-4)}&=\frac{\frac{9}{2}-1}{3 + 4}\ &=\frac{\frac{9-2}{2}}{7}\ &=\frac{\frac{7}{2}}{7}\ &=\frac{1}{2} \end{align*} ]

Answer:

A. (\frac{1}{2})