how to add curves? (1 Viewer)

[kpq_sniper017]

how exactly do u add curves?
e.g. e^x + e^-x (got this from another post).

i dont think ive done "adding curves" for curve-sketching.
but how do u look at one curve, look at the other and "add them"?

 

[untamedanimal]

Its not that hard really. You draw the first graph, y = e^x, draw the second one on the same graph, y = e^-x and make sure the scale is the same. The you just add the y values of the curve. Say at x = 1, y = e^1 + e ^-1. You just do these for the important points of the graph, like when an axis is cut. I dont know if you do physics, but if you do, the method is similar to the prelim topic of waves, where you add two waves together, its exactly the same thing

 

[Jase]

like untamed said, its quite simply the addition of the Y-values.

e.g. , points of intersection are moved up twice the original value.
etc.., one Y value of one graph plus the Y value of another graph will become the Y value of the new graph. (did that make sense?)

for 3 unit, its best to find all turning points for any graph. (unless it doesnt have any), find all asymptotes, and then substitute for points that youre unsure of. At least, i think thats the safe way.

Only use addition/multiplication of ordinates if if asks you to, or if its only for better understanding of the question, or if theres really no easy way of doing it and your lazy. (like me)

anyway, just practice adding graphs. Draw out a table of values if you must. Thats practically the basic concept behind adding ordinates anyway, your just using a table of values in your head.

 

[Xayma]

It is easiest to do ordinate addition, however if you want (and I dont think it works with this graph but it does with some others) you can find limits and stat points. For example as e^x+e^-x gets very large the graph approaches e^x