Question

Given the parent function of f(x) = x^(4, what change will occurr when the function is changed to f((1)/(2) x))

Answer 1

The graph of the function f( (1/2)x ) will expand across x-axis

Explanation:

We have been given the function:

f(x) = x⁴

If we substitute x = (1/2)x into the given equation, we get:

f((1/2)x) = ( (1/2)x )⁴

We can simplify the equation

f((1/2)x) = = (1/2)⁴ x⁴

f((1/2)x) = = (1/16) x⁴

Graph of both of the functions is shown below. We can clearly see that that the graph of the function f((1/2)x) = = (1/16) x⁴ expands horizontally on x-axis as compared to the graph of f(x) = x⁴