How do you graph #y=1/2e^x+1#?

1 Answer

Start with the graph for #e^x#, then adjust for the 1/2 and +1


When graphing functions, find the "base function", then adjust for the modifiers.

In this case, the base function is #e^x# and that looks like this:

graph{e^x [-5, 5, -5, 5]}

The first adjustment we'll make is for the 1/2. See the y-intercept at (0,1)? That's going to change to (0,1/2) and the graph is going to rise at 1/2 the rate of #e^x#:

graph{(1/2)e^x [-5, 5, -5, 5]}

And now let's finish up by lifting the graph 1 unit upward to account for the +1:

graph{(1/2)e^x+1 [-5,5,-5,5]}