How do you graph #y=2^(x+1)+3#?

1 Answer

The new coordinates would be

#(-2,3.5)#, #(-1,4)#, #(0,5)#, #(1,7)#, #(2,11)#

Explanation:

First, you want to know some points for the parent function, #y=2^x#

  • #(-1,.5)#
  • #(0,1)#
  • #(1,2)#
  • #(2,4)#
  • #(3,8)#

graph{2^x [-10, 10, -5, 5]}

Then we can look at this new equation and see that the y-intercept shifts up 3 from the #+3#, so all the y coordinates shift up #3# as well.

We also can see that the x coordinates all shift left 1 from the #x+1#. The new coordinates would be

  • #(-2,3.5)#
  • #(-1,4)#
  • #(0,5)#
  • #(1,7)#
  • #(2,11)#

graph{2^(x+1) + 3 [-9.92, 10.08, -0.8, 9.2]}