Rewrite the radical function g(x)= ^3 √8x+56 +4 to identify the transformations from the parent function's graph f(x)= ^3 √x?
Pretty sure you would find inverse but not sure how to do it
∛(8x+56) = ∛(8(x+7))
= 2∛(x+7)
so, shift left 7, scale y by 2 and shift up 4
To rewrite the radical function g(x) = ∛(8x+56) + 4 in terms of the parent function f(x) = ∛x, we need to identify the transformations.
The parent function f(x) = ∛x represents a basic cube root function, where the input (x) value is raised to the power of 1/3.
Let's break down the transformations and how they affect the equation:
1. Horizontal Transformation:
The function g(x) = ∛(8x+56) + 4 has a horizontal transformation compared to the parent function f(x) = ∛x. By observing the argument inside the cube root, 8x+56, we can see that the original function has been horizontally compressed or stretched by a factor of 8. This means that the transformation moves the graph horizontally compared to the parent function.
2. Vertical Transformation:
The function g(x) = ∛(8x+56) + 4 also has a vertical transformation compared to the parent function f(x) = ∛x. Here, the cube root function has been "shifted vertically," shifting the entire graph upward by 4 units. Thus, the graph of g(x) is higher than the graph of f(x) by 4 units.
To summarize the transformations from the parent function f(x) = ∛x to the function g(x) = ∛(8x+56) + 4:
1. Horizontal Transformation: The graph is horizontally compressed or stretched by a factor of 8.
2. Vertical Transformation: The graph is shifted upward by 4 units.
Note: The process mentioned above helps identify the transformations. If your intention is to find the inverse function, it requires a different approach.