Hoiw do you graph log and exponential fns? (1 Viewer)

[rsingh]

How do you graph log and exponential fns?

Hey guys,

I'm really crap at graphing log and exponential fns. In fact, I can't do them at all! I've seen some of the 2u questions and I think once I get the hang of it I can do those, however the 3u ones are just beyond me at the moment.
Could someone give me a rundown how to graph log and exponential fns, and the relationship between them? (I know there inverses of one another but I'm sure there's more?)

Thanks.

 

[who_loves_maths]

you need to simply remember the basic form of the exponential and log functions in their standard form (ie. y=lnx , y=e^x) and then apply approriate transformations on them depending on the function you're given.

if you can give a specific example of a graph you're having trouble with, that'd be good.

 

[rsingh]

Ok then, umm .. how would I graph something like:

y=In(x-2)
y=xInx
y=2e^2x

??
I'm totally confused. I mean, generally, how would you transfer the graphs?
And while we're at it, I've seen some questions (not on logs and exponentials but in general) where they give you the eqt of a graph and tell you that it has been shifted/translated in some way, and your required to give the new eqt of the graph? How would you do that?

 

[acmilan]

Ok then, umm .. how would I graph something like:

y=In(x-2)

When in the form y = ln(x - a), you shift the graph to the right a unit, when y = ln(x + a), you shift it to the left a units. Graph below (green: y = ln(x+2), blue: y = lnx, red: y = ln(x-2))

 

[acmilan]

y=xInx

This one probably wouldnt appear in 3 unit. What you could do is work out the turning point and concavity and draw it like you would an ordinary graph, remembering that x cannot be negative. You could also draw the graph of y = x and y = lnx, and then multiple various points on the graph to get y = xlnx. Graph below (blue: y = x, green: y = xlnx, red: y = lnx)

 

[acmilan]

y=2e^2x

This one would like very similar to y = e^x. Graph below (blue: y = e^x, green: y = 2e^2x, red: y = e^2x)

 

[rsingh]

Thanks acmilan. You're a champ! I appreciate it very much!
So in general, if there is a constant infront of a log or exponential, how does that affect the graph?

Also, what types of logs/exp graphs can we expect for 2u and 2u respectively?

 

[who_loves_maths]

hahaha... love the visual effects acmilan

 

[acmilan]

Thanks acmilan. You're a champ! I appreciate it very much!
So in general, if there is a constant infront of a log or exponential, how does that affect the graph?

Also, what types of logs/exp graphs can we expect for 2u and 2u respectively?

They affect the steepness of the graph. The larger the constant, the steeper it would be. Also for exponential graphs it affects where it cuts the y-axis, graphs in the form y = ae^bx, where a and b are constants, will cut the y-axis at a.

 

[rsingh]

Ok, but I'm still not quite sure.
If the 'a' or 'b' changes, then what happens? How does each constant affect the graph? Which one affects the steepness? What does the other one do?

 

[acmilan]

They both change the steepness. Remember that the steepness is determined by the first derivative. At any point x, the gradient at that point on the line y = ae^bx is y' = abe^bx. Hence a change in either a or b will change the steepness of the graph.

 

[rsingh]

Oh, that's right. I've never thought of it that way.
Isn't that true for all graphs, the gradient determines the steepness at a particular point?
Does the second derivative have any more significance than just determining the concavity of a graph?

 

[SeDaTeD]

Well, actually the b would determine the horizontal scaling, ie it would squish the graph horizontally by a factor of b. So the places where it cuts the x-axis will also move (in cases where x is replaced by bx).