How do you graph f(x)=2(x+1)^3-2 ?

f(x)=2(x+1)^3-2

To start with it is a cubic.  Because the 2 out  the front is positve it will start in the first  quadrant and finish in the third quadrant.

a)  It will look like y=x^3   (The only root is at x=0)   THIS WILL CHANGE

b)  The +1 will make it move 1 unit  to the LEFT  (at this point in the exercise  x=-1 will be the root)

c)   The factor of 2 out the front will strech it in a viertical direction so ever point is twice the perpendicular distance from the the x axis.

d) the -2 at the end will drop every point down by 2 units

I shall show you with the 4 graphs.

You could plot some points. Work out what value f(x) has when x is -2, -1, 0, +1 and if you need another point, try when x is +1.5

Then plot f(x) on the vertical axis, against x on the horizontal axis.