Question

Find the equation of the function (g(x)) resulting from (f(x) = x^3) undergoing the following transformations, in order:

1. shifted to the right by 3 units
2. reflected across the x-axis
3. shifted downward by 10 units.

A) (g(x) = -(x - 3)^3 + 10)
B) (g(x) = -(x + 3)^3 - 10)
C) (g(x) = -(x + 3)^3 + 10)
D) (g(x) = (x - 3)^3 - 10)

Answer 1

The correct function for g(x) after undergoing the specified transformations on f(x) = x^3 is D) g(x) = (x - 3)^3 - 10.

Step-by-step explanation:

To find the equation of the function g(x) resulting from the transformations applied to f(x) = x^3, we perform the following steps:

1. Shift the graph to the right by 3 units: f(x) becomes f(x - 3), so g(x) = (x - 3)^3.
2. Reflect the graph across the x-axis: This negates the function, transforming it to g(x) = -(x - 3)^3.
3. Shift the graph downward by 10 units: This subtracts 10 from the function, resulting in g(x) = -(x - 3)^3 - 10.

Comparing the sequences of transformations with the given options, the correct function for g(x) is D) g(x) = (x - 3)^3 - 10.