The function f(x) = x⁵ after being reflected across y = x and shifted up 2 units becomes g(x) = x⁵ + 2.
How to find the function?
Reflect across the line y = x:
This swaps the x and y axes, essentially making y the function of x. In mathematical notation, it's represented as g(x) = f(y).
So, after reflection, there is g(x) = f(x). Remember, f(x) is still x⁵.
Shift up 2 units:
This vertically translates the graph upwards by 2 units. In mathematical notation, it's represented as g(x) = f(x) + 2.
Therefore, the resulting function after applying both transformations is:
g(x) = x⁵ + 2
Which function results after applying the sequence of transformations to
f(x) = x⁵?
• reflect across the line y = x
• shift up 2 units