<h2>
Answer:</h2>
The average rate of change in f(x) over the interval [1, 5] is -1
<h2>
Step-by-step explanation:</h2>
Hi! Let me help you to understand this problem. Here we have the following function:
![f(x) = 17-x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2017-x)
We need to compute the Average Rate of Change (ARC) in
over the interval
. So <em>what is the average rate of change of a function? </em>In general, for a nonlinear graph whose slope changes at each point, the average rate of change between any two points
is defined as the slope of that line through that two points. Here we have a linear function, so the average rate of change will be the slope of the line:
So:
![ARC=m=-1](https://tex.z-dn.net/?f=ARC%3Dm%3D-1)
This can also be calculated as:
Start by expanding the left side of the equation: -2(4x-7) is equal to -8x + 14.
This brings you to -8x+14 = -8x + 14.
Now add 8x to both sides. This brings you to 14 = 14
Now subtract 14 from both sides. This brings you to 0 = 0.
Thus your answer is 0 = 0, which is a true statement.
Hope this helps.
Answer:
The slope is -3/2 (
)
Step-by-step explanation:
I hope this helps! :)
as you should already know to get the inverse of any expression, we start off by doing a <u>quick switcheroo</u> on the variables, and then solve for "y".
![\bf \stackrel{f(x)}{y} = \cfrac{x}{x-1}\implies \stackrel{switcheroo}{x=\cfrac{y}{y-1}}\implies x(y-1)=y\implies xy-x=y \\\\\\ -x=y-xy\implies -x=\stackrel{\textit{common factor}}{y(1-x)}\implies \cfrac{-x}{1-x}=y \\\\\\ \cfrac{x}{-(1-x)}=y\implies \cfrac{x}{x-1}=\stackrel{f^{-1}(x)}{y}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bf%28x%29%7D%7By%7D%20%3D%20%5Ccfrac%7Bx%7D%7Bx-1%7D%5Cimplies%20%5Cstackrel%7Bswitcheroo%7D%7Bx%3D%5Ccfrac%7By%7D%7By-1%7D%7D%5Cimplies%20x%28y-1%29%3Dy%5Cimplies%20xy-x%3Dy%20%5C%5C%5C%5C%5C%5C%20-x%3Dy-xy%5Cimplies%20-x%3D%5Cstackrel%7B%5Ctextit%7Bcommon%20factor%7D%7D%7By%281-x%29%7D%5Cimplies%20%5Ccfrac%7B-x%7D%7B1-x%7D%3Dy%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7Bx%7D%7B-%281-x%29%7D%3Dy%5Cimplies%20%5Ccfrac%7Bx%7D%7Bx-1%7D%3D%5Cstackrel%7Bf%5E%7B-1%7D%28x%29%7D%7By%7D)
2. 3/4 yards
3.18 miles 210 yards
4. 4 yards 2 feet and 3 inches
5. 9 lbs 2oz
6. 10 tons 1400 lbs
7. 18 gallons 1 quart
8. 5pt 10 fluid ounces