is referred to as a cubic function. We shall also refer to this function as the "parent" and the following graph is a sketch of the parent graph.
and their graphs.
The parent graph is shown in red and the variations of this graph appear as follows: the function y = f(x) + 2 appears in green; the graph of y = f(x) + 5 appears in blue; the graph of the function y = f(x) - 1 appears in gold; the graph of y = f(x) - 3 appears in purple. It is now easy to generalize: If y = f(x) + c and c > 0, the graph undergoes a vertical shift c units up along the y-axis. If y = f(x) + c and c < 0, the graph undergoes a vertical shift c units down along the y-axis.
Now, let's examine the graphs and make our observations.
As before, our parent graph is in red, y = f(x + 1) is shown in green, y = f(x + 3) is shown in blue, y = f(x - 2) is shown in gold, and y = f(x - 4) is shown in purple. Let's make our observations: If y = f(x + d) and d > 0, the graph undergoes a horizontal shift d units to the left. If y = f(x + d) and d < 0, the graph undergoes a horizontal shift d units to the right.
is called a cubic function. Consider the function
1) If c > 0, the graph shifts c units up; if c < 0, the graph shifts c units down. 2) If d > 0, the graph shifts d units to the left; if d < 0, the graph shifts d units to the right.