A function f is given and the indicated transformation are applied to its graph (in the given order) write the equation for the final transformed graph f(x)=4 under root x reflect in the y axis and shift upward 6 units

Question

Then y=?

Answer 1

To find the equation for the final transformed graph, we need to apply each transformation to the original function f(x) = 4√x in the given order.

1. Reflect in the y-axis:
Reflecting a function in the y-axis simply changes the sign of the x-values. Therefore, the reflection of f(x) = 4√x becomes f(-x) = 4√(-x).

2. Shift upward 6 units:
Shifting a function upward means adding a constant value to the y-values. So, the shift of f(-x) = 4√(-x) upward by 6 units becomes f(-x) + 6 = 4√(-x) + 6.

Therefore, the equation for the final transformed graph is:
f(-x) + 6 = 4√(-x) + 6.

Now, to find y, we can simply substitute x for -x in the equation. This will give us the value of f(x) for any given x-coordinate.

Hence, y = f(x) + 6 = 4√x + 6.