A function f is given and the indicted transformation are applied to its graph write the equation for the final transformed graph
F(x)=3 under root x shift 7 units to the right
Then y=?
To find the equation for the final transformed graph, we need to apply each transformation step by step.
The function f(x) = √(x) represents the square root function.
1. Shift 7 units to the right:
The function g(x) = f(x - 7) represents a shift of 7 units to the right. To perform this transformation, we substitute (x - 7) for x in the function f(x), which gives us g(x) = √(x - 7).
2. Multiply by 3:
The function h(x) = 3g(x) represents a vertical stretch by a factor of 3. To perform this transformation, we multiply the function g(x) by 3, which gives us h(x) = 3√(x - 7).
Therefore, the equation for the final transformed graph is y = 3√(x - 7).
To shift the graph of the function f(x) = √x seven units to the right, we need to replace x with (x - 7) in the equation.
The new equation for the transformed graph would be:
f(x) = √(x - 7)
To include the additional transformation F(x) = 3, we simply add 3 to the equation:
y = f(x) + 3
Therefore, the equation for the final transformed graph is:
y = √(x - 7) + 3
To find the equation for the final transformed graph, we need to apply the given transformations step by step to the original function.
The original function is f(x) = 3√x.
1. Shifting 7 units to the right:
To shift the graph 7 units to the right, we need to replace x with (x - 7) in the function. This will cause the graph to move to the right by 7 units.
f(x) = 3√(x - 7)
Therefore, the equation for the graph after shifting 7 units to the right is f(x) = 3√(x - 7).
If you are looking for the value of y in terms of x, you can replace f(x) with y.
y = 3√(x - 7) is the equation for the final transformed graph.