Answer:
graph b
Step-by-step explanation:
it's b because it doesn't have any features like a function it's just a round shape that makes it a none function
![f'(x)=\dfrac{4x}{1+7x^2}](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cdfrac%7B4x%7D%7B1%2B7x%5E2%7D)
Integrating gives
![f(x)=\displaystyle\int\frac{4x}{1+7x^2}\,\mathrm dx](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%5Cint%5Cfrac%7B4x%7D%7B1%2B7x%5E2%7D%5C%2C%5Cmathrm%20dx)
To compute the integral, substitute
, so that
. Then
![f(x)=\displaystyle\frac27\int\frac{\mathrm du}u=\frac27\ln|u|+C](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdisplaystyle%5Cfrac27%5Cint%5Cfrac%7B%5Cmathrm%20du%7Du%3D%5Cfrac27%5Cln%7Cu%7C%2BC)
Since
for all
, we can drop the absolute value, so we end up with
![f(x)=\dfrac27\ln(1+7x^2)+C](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac27%5Cln%281%2B7x%5E2%29%2BC)
Given that
, we have
![10=\dfrac27\ln1+C\implies C=10](https://tex.z-dn.net/?f=10%3D%5Cdfrac27%5Cln1%2BC%5Cimplies%20C%3D10)
so that
![\boxed{f(x)=\dfrac27\ln(1+7x^2)+10}](https://tex.z-dn.net/?f=%5Cboxed%7Bf%28x%29%3D%5Cdfrac27%5Cln%281%2B7x%5E2%29%2B10%7D)
Answer:Geometry allows students to connect mapping objects in the classroom to real-world contexts regarding direction and place. Understanding of spatial relationships is also considered important in the role of problem solving and higher-order thinking skills.
Step-by-step explanation: