Question

Use complete sentences to explain the process of graphing f(x) = –x^3 + 1.

Answer 1

Well, the first thing to notice about the function is that its "parent" function is \[f(x)=x^3\]After more experience and maybe some memorization, one will be able to recognize the graphs of most parent functions. Now we look at whether it is negative of positive. In this case it it negative, meaning that the graph will be decreasing from left to right. Now that we know the general shape of the function and whether it is flipped or not, we can see if it is shifted along the y-axis or the x-axis. In this case, there is only a constant of 1 on the end which means the entire graph will be shifted up by 1. I'll attach a graph of the parent function and the modified function. The parent function is black and f(x)=-x^3+1 is in red.