Answer:
Yes
Step-by-step explanation:
Reflections and translations are instances of transformation.
<em>The rule of function g for the given reflection and translation is </em>
<em />
<em />
Given
![f(x) = 6x](https://tex.z-dn.net/?f=f%28x%29%20%3D%206x)
<u>The rule of translating 5 units up is:</u>
![(x,y) \to (x,y+5)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28x%2Cy%2B5%29)
So, we have:
![f'(x) = f(x) +5](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20f%28x%29%20%2B5)
![f'(x) = 6x +5](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%206x%20%2B5)
<u>The rule of reflecting about the y-axis is:</u>
![(x,y) \to (-x,y)](https://tex.z-dn.net/?f=%28x%2Cy%29%20%5Cto%20%28-x%2Cy%29)
So, we have:
![g(x) =f(-x)](https://tex.z-dn.net/?f=g%28x%29%20%3Df%28-x%29)
![g(x) =6(-x) + 5](https://tex.z-dn.net/?f=g%28x%29%20%3D6%28-x%29%20%2B%205)
![g(x) =-6x + 5](https://tex.z-dn.net/?f=g%28x%29%20%3D-6x%20%2B%205)
Hence, the rule of function g is: ![g(x) =-6x + 5](https://tex.z-dn.net/?f=g%28x%29%20%3D-6x%20%2B%205)
Read more about function transformations at:
brainly.com/question/13801312
we know that
The vertex of the function
is the point ![(0,0)](https://tex.z-dn.net/?f=%280%2C0%29)
The vertex of the function
is the point ![(4,-2)](https://tex.z-dn.net/?f=%284%2C-2%29)
The x-coordinate of the vertex is equal to h
the y-coordinate of the vertex is equal to k
so
the value of h is ![4](https://tex.z-dn.net/?f=4)
the value of k is ![-2](https://tex.z-dn.net/?f=-2)
the equation is
![f(x)=(x-4)^{2}-2](https://tex.z-dn.net/?f=f%28x%29%3D%28x-4%29%5E%7B2%7D-2)
therefore
<u>the answer is the option a</u>
![4](https://tex.z-dn.net/?f=4)
Answer:
Small one is 4ft larger one is 12ft