Answered

Get the answers you need from a community of experts on IDNLearn.com. Our experts are available to provide accurate, comprehensive answers to help you make informed decisions about any topic or issue you encounter.

given g(x) = −3x + 4
(a) Find the average rate of change of the function between
for x = a
and
x = a + h.

Sagot :

XKelvinidn

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.

We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.