Liz Z. answered • 09/16/20

Trig is cool!

For b(x)=(x+2)^{3}, the parent function is y=x^{3}, which looks a lot like x^{2}, but steeper, and the part to the left of the y-axis goes down instead of up. (When we square negative numbers, they become positive, but cubing a negative number results in another negative number.) The 2 added *inside the parentheses to the x *moves the function left 2, because whatever is added or subtracted to the x in parentheses always does the opposite. Instead of a critical point at (0,0), this function has a center at (-2,0). There are no asymptotes; the domain and range are both (-∞,∞). I can't graph the function here, but you can do that at https://www.desmos.com/calculator.

I hope this helps!

Liz Z.