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
Then y=?
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.
To find the equation for the final transformed graph, we can break down the given transformations and apply them step by step.
Step 1: Reflect in the y-axis
When we reflect a graph in the y-axis, we change the sign of the x-coordinate. So, if the original function is f(x), the reflected function will be f(-x).
Step 2: Shift upward 6 units
To shift a graph upward, we add a constant to the original function. So, if the original function is f(x), the shifted function will be f(x) + c, where c is the constant.
Given that the original function is f(x) = 4√x, let's apply the transformations step by step:
Step 1: Reflect in the y-axis
The reflected function is f(-x) = 4√(-x).
Step 2: Shift upward 6 units
The final transformed function is f(-x) + 6 = 4√(-x) + 6.
Now, let's simplify the equation:
f(-x) + 6 = 4√(-x) + 6
f(-x) = 4√(-x)
Therefore, the equation for the final transformed graph is f(x) = 4√(-x).
Finally, to find y, you can simply replace f(x) with y in the equation:
y = 4√(-x)
To find the equation for the final transformed graph, we will apply each transformation to the original function f(x)=4.
1. Reflecting in the y-axis:
Reflecting a function in the y-axis involves changing the sign of x. Therefore, our new function after reflecting will be f(-x)=4.
2. Shifting upward 6 units:
To shift the function upward, we need to add a constant value to the original function. Since we want to shift it upward by 6 units, our final transformed function will be f(-x) + 6 = 4 + 6 = 10.
So, the equation for the final transformed graph is y = f(-x) + 6 = 10