Transformations of Exponential Functions Part 1

This lesson demonstrates how to work with transformations of Exponential Functions. This is the first part of a two part lesson. This lesson was created for the MCR3U Functions course in the province of Ontario, Canada.

[nocturnalman]

thanks Richard, you're a better teacher than my prof.

[AlRichards]

For y=2^(x+3) it is moved 3 left because if 3 is added to the x in the equation, then in order for the function to have the same y value (for any point) then that point must have an x 3 smaller. If this point's x coordinate is 3 smaller then it is moved 3 to the left. For example on y=2^x the first point plotted was (3, 8) since 2^3 = 8. On y=2^(x+3) in order for a point to have the same y=8 we have to make the x=3, 3 smaller, so the point is (3-3, 8) or (0, 8) & (0, 8) is 3 units left of (3, 8).

[AlRichards]

@MrXitomate A transformation is a graphical change in the function or curve. What that means is the function might be moved up or down, which is normally called a vertical or horizontal translation (translations move side to side or up/down. The graph might be stretched vertically (or compressed). That means for any ordered pairs the x's stay the same but the y's are multiplied by some constant or divided.
The other common transformation is it might be reflected in either the x or y axis.

[AlRichards]

@OnZMark The a, k, d and c are used for these transformations basically as a convention. So, only for the reason, that this is the normally accepted way of writing them are a, k, d and c used. And thanks for the comment.

[AlRichards]

If the x value is divided by 30 then that's a horizontal stretch. For example in y = 2^(x/30), then all the points on the curve would be 30 times further from the y axis than for y = 2^x.

[girlygirl]

You explain this much better than my teacher!

[miningking]

Thanks so much for this info, I was very confused when doing this. Im having a test on this stuff, wish me luck everyone!

[Queentwig]

These are great videos! Very helpful! Thanks!

[Mike-ksqu]

By far the most comprehensive explanation of transformations. I knew what they would look like graphically but my book didn't explain how. 

[nicoargca]

WOW, excellent explanation from the first moment the video starts.

[MatthewDadoun]

Thanks so much, I actually happen to be taking MCR3U and it's painful. Real painful.

[AlRichards]

Not necessarily. I create a table of values for the original function and transform the table to graph the transformed function.

[AlRichards]

I believe I showed both y= 3^x and y = (1/3)^x in the video - first & second pages. However, they are reflections of each other in the y-axis.

[AlRichards]

@sc092270 I draw almost all of my graphs in PowerPoint. Specifically, the curve tool works well to duplicate mathematical curves. Sometimes it takes a few trys before I get the exact shape I want, but it works well for my purposes. The nice thing about it is that once you have the basic shape, any other related curves are just stretches, so you can use the original curve for that.

[sc]

What software do you use for your graphs?

[OnZMark]

I've noticed a few videos that use A B C D rather than A K D C for the constant parameters, is there a critical reasoning behind the latter nomenclature?

Great work as always!

[Jabbawockeez]

thumbs up from my side! really gud explanation, now i have my math exam tomorrow

[RaffaelloLorenzusSayde]

What about for horizontal reflection and horizontal compress or stretch? Also, is it like this for transforming 2^x to y=-2(2^-2x-3)-1 using this method for table of values (x, y) for x it's (k, d) and for y it's (a, c)? The form for exponential functions is y=a×b^k(x-d)+c.

[AlRichards]

For any function when the x is multiplied by -1, that's a reflection in the y axis.

[billz]

This helped so much!!!!

You should do Transformations of Logarithmic Functions.