By using transformations sketch the graph of the given functions.
h ( x ) = ( x + 2)^{3}
Solution
With these we have to first identify the "base" function. i.e. the function that's being shifted. In this case it seem like we are shifting f ( x ) = x^{3} . Then we can see that,
h ( x ) = ( x + 2)^{3 }= f (x + 2)
In this case c = 2 and thus we're going to shift the graph of f ( x ) = x^{3} (the dotted line on the graph below) & move it 2 units to the left. It will mean subtracting two from the x coordinates of all the points on f ( x ) = x^{3} .
Following is the graph for this problem.