Answer: Option D
g(x) is shifted 3 units to the left and reflected over the x-axis.
Step-by-step explanation:
If we have a main function ![f (x) = x ^ 4](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%20x%20%5E%204)
And we perform the transformation:
![g (x) = f (x + h) = (x + h) ^ 4](https://tex.z-dn.net/?f=g%20%28x%29%20%3D%20f%20%28x%20%2B%20h%29%20%3D%20%28x%20%2B%20h%29%20%5E%204)
Then it is fulfilled that:
If
the graph of f(x) moves horizontally h units to the left
If
the graph of f(x) moves horizontally h units to the right
If we have a main function ![f (x) = x ^ 4](https://tex.z-dn.net/?f=f%20%28x%29%20%3D%20x%20%5E%204)
And we perform the transformation:
![g (x) = -f(x) = -x ^ 4](https://tex.z-dn.net/?f=g%20%28x%29%20%3D%20-f%28x%29%20%3D%20-x%20%5E%204)
Then it is fulfilled that:
The graph of g(x) is equal to the graph of f(x) reflected on the x axis
In this case we have to:
and ![f(x) = x^4](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E4)
Therefore
and ![g(x) = -f(x)](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-f%28x%29)
This mean that: g(x) is shifted 3 units to the left and reflected over the x-axis.