How do you graph f(x)= e^-(x+2) if x is less than -2 ; f(x)= e^(x+2) if x is greater than or equal to -2.

Question

I just need a breakdown of how to graph this.

f(x)=

( e^-(x+2) if x is less than -2

e^(x+2) if x is greater than or equal to -2 )

Answer 1

HI Jac,

When we plug in x = -2 we get e⁰ which equals 1, so plot a point at (-2, 1). Notice that both pieces of the equation would be 1 if we plugged in x = -2 so both pieces will touch the point we just plotted.

The first piece f(x) = e^-(x+2) is a steep downward-sloping curve so put the pencil just to the left of x = -2 but very high (infinity), then swoop down with a slight curve into the point (-2, 1).

The second piece does the reverse, so start with the pencil on the point (-2, 1) and swoop it up toward infinity with a slight curve.

Please let me know if I can be more helpful, thanks!

Joe

Answer 2