Describe how the graph of g(x)equalsRootIndex 3 StartRoot x EndRootminus5 can be obtained from the graph of f(x)equalsRootIndex 3 StartRoot x EndRoot. Then graph the function g(x).
To obtain the graph of g(x) from the graph of f(x), we need to shift the graph of f(x) five units to the right. This means the graph of g(x) will have the same shape as f(x), but it will be shifted five units to the right.
The function g(x) = cube root(x - 5) can be graphed as follows:
- Start by plotting the point (5, 0) which is the new x-intercept after shifting f(x) to the right by 5 units.
- Since g(x) is a cube root function, it will have the same cubic shape as the f(x) function but shifted to the right.
- Connect the point (5, 0) to the rest of the graph in a cubic shape moving towards the origin (0, 0).
The graph of g(x) = cube root(x - 5) will look like a cubic function flipped upside down and shifted five units to the right compared to the graph of f(x) equals the cube root of x.