help: harder exponential sketching (1 Viewer)

[+GriM ReApeR+]

How do you graph harder exponentials, like y = e^x + e^-x ??

Thanks...

 

[CM_Tutor]

Two easy methods - (1) Sketch y = e^x and y = e^-x, and then add them together.

(2) - Use the curve sketching menu I posted about recently.

In this case, the function is even, continuous and differentiable, so it has a turning point at its y-intercept. For x > 0, 0 < e^-x < 1, but e^x is increasing rapidly, so it looks a lot like y = e^x for x > 0 (in shape), except that it is horizontal at (0, 2). Since it's even, just reflect across the y-axis - In summary, it has basically the same sketch as y = x² + 2.