Answer:
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Answer:
Third option.
Step-by-step explanation:
Some transformations for a function f(x), are:
If 
, the function is shifted down "k" units.
If 
, the function is shifted up "k" units.
If 
, and 
, the functio is stretch vertically by a factor of "b".
If 
, the function is reflected over the x-axis.
Therefore, knowing that the parent function 
was transformated by reflecting it over the x-axis, stretching vertically by a factor of 2 and shifting it down 3 units, we can determine that the following function represents the transformation:
The length of the curve 
from x = 3 to x = 6 is 192 units
<h3>How to determine the length of the curve?</h3>
The curve is given as:
from x = 3 to x = 6
Start by differentiating the curve function
Evaluate
The length of the curve is calculated using:
This gives
![L =\int\limits^6_3 {\sqrt{1 + [x(9x^2 + 6)^\frac 12]^2}\ dx](https://tex.z-dn.net/?f=L%20%3D%5Cint%5Climits%5E6_3%20%7B%5Csqrt%7B1%20%2B%20%5Bx%289x%5E2%20%2B%206%29%5E%5Cfrac%2012%5D%5E2%7D%5C%20dx)
Expand
This gives
Express as a perfect square
Evaluate the exponent
Differentiate
Expand
L = (6³ + 6) - (3³ + 3)
Evaluate
L = 192
Hence, the length of the curve is 192 units
Read more about curve lengths at:
brainly.com/question/14015568
#SPJ1
Answer:
-1.
Step-by-step explanation:
First, you find the distance from the first x coordinate to the second. This is done by doing -5 - -1 (aka -5 + 1), which equals -4. Then, you find the distance form the first y coordinate to the second. THis is done by doing 0 - -4 (aka 0 + 4), which equals 4. Then, you divide the distance of the y's over the distance of the x's, which gets you the slope, which is -1. Hope this helped!
