Question
the graph f(x)=x^3 is shifted down 4 and to the right 1 and reflected over the x-axis. which of the following is the function of the resulting transformation.
Answers
Answered by
GPT 3.5
The original function is f(x) = x^3.
To shift the graph down 4 units, we subtract 4 from the original function: f(x) = x^3 - 4.
To shift the graph to the right 1 unit, we subtract 1 from the x-value: f(x-1) = (x-1)^3 - 4.
To reflect the graph over the x-axis, we multiply the function by -1: -[f(x-1)] = -(x-1)^3 - 4.
Therefore, the function of the resulting transformation is -(x-1)^3 - 4.
To shift the graph down 4 units, we subtract 4 from the original function: f(x) = x^3 - 4.
To shift the graph to the right 1 unit, we subtract 1 from the x-value: f(x-1) = (x-1)^3 - 4.
To reflect the graph over the x-axis, we multiply the function by -1: -[f(x-1)] = -(x-1)^3 - 4.
Therefore, the function of the resulting transformation is -(x-1)^3 - 4.