Let's describe the transformation of the function f (x) = x^3
The parent function is the simplest form of the type of function given.
g (x) = x^3 → f (x) = x^3
The horizontal shift depends on the value of h. The horizontal shift is described as:
• f (x) = f (x + h) The graph is shifted to the left h units
,
• f (x) = f (x - h) The graph is shifted to the right h units
,
• In this case, h = 0, which means that the graph is not shifted to the left or right.
Horizontal Shift: None
The vertical shift depends on the value of k. The vertical shift is described as:
• f (x) = f (x) + k The graph is shifted up k units
,
• f (x) = f (x) - k The graph is shifted down k units
,
• In this case, k = 0, which means that the graph is not shifted up or down.
Vertical shift : None
The graph is reflected about the x-axis when f (x ) = - f (x)
Reflection : None
The graph is reflected about the y-axis when f (x) = f (-x)
Reflection : None