Answer:
The average rate of change of g from x = a to x = a + h is -3.
Step-by-step explanation:
We are given the function:
[tex]g(x) = -3x + 4[/tex]
And we want to determine its average rate of change of the function for x = a and x = a + h.
To determine the average rate of change, we find the slope of the function between the two points. In other words:
[tex]\displaystyle \text{Avg} = \frac{g(a + h) - g(a) }{(a + h ) - a}[/tex]
Simplify:
[tex]\displaystyle \begin{aligned} \text{Avg} &= \frac{g(a + h) - g(a) }{(a + h ) - a} \\ \\ &=\frac{(-3(a+h) + 4) - (-3a+4)}{h} \\ \\ &= \frac{(-3a -3h + 4) + (3a - 4) }{h} \\ \\ &= \frac{-3h}{h} \\ \\ &= -3\end{aligned}[/tex]
In conclusion, the average rate of change of g from x = a to x = a + h is -3.
This is the expected result, as function g is linear, so its rate of change would be constant.
