How do you move a cubic function to the left, right or vertically?
To the left - add the number of units you wish to move it. ex. 2 units f(x) = (x + 2)3
To the right - subtract the number of units you wish to move it. ex. 3 units f(x) = (x - 3)3
Vertically up - add the number of units you wish to move it. ex. 4 units f(x) = x3 + 4
Vertically down - subtract the number of units you wish to move it. ex. 6 units f(x) = x3 - 6
Below is the graph of the parent function. f(x) = x3
Below is the graph of the function f(x) = (x - 2)3 + 1
Notice that to moved the parent function two places to the right we subtracted 2 from the x
and enclosed the result in a set of parentheses with the exponent 3 outside.
Next we added one outside the parentheses to move the graph up one unit.