Specify the sequence of transformations that will yield the graph of the given function from the graph of the function f(x)=x^3.
g(x)=-(x-4)^3
My answer was a vertical shrink and a reflection in the y-axis but I think this is wrong.
a horizontal shift of 'slide' of 4 units to the right, then a reflection in the x-axis
To determine the sequence of transformations that will yield the graph of the function g(x) = -(x-4)^3 from the graph of the function f(x) = x^3, you first need to understand the effect of each transformation.
1. Translation:
The function g(x) = -(x-4)^3 is obtained by horizontally shifting the graph of f(x) = x^3 to the right by 4 units. This means that the entire graph will be moved four units to the right.
2. Reflection:
The negative sign in front of the entire function g(x) reflects the graph of f(x) = x^3 across the x-axis. This results in the graph being flipped upside down.
Therefore, the correct sequence of transformations to obtain g(x) = -(x-4)^3 from f(x) = x^3 is:
1. Translate four units to the right.
2. Reflect the graph across the x-axis.
So, your initial answer of a vertical shrink and a reflection in the y-axis is incorrect. It should be a horizontal translation and a reflection across the x-axis.