1. Transformations
When I look at something like f(x+3)-2, I first consider what is inside the parenthesis. Whatever is in the parenthesis will determine how the graph will shift horizontally. Since there is a +3, the graph will shift to the left by 3. You will think that because it a positive number you would shift the graph to the right but NO. I just remember to do the opposite when I am looking inside the parenthesis.
Next, I look outside the parenthesis to determine how the graph will shift vertically. Now that I am not looking inside the parenthesis, I can go with my normal instincts and shift the graph up or down by the number indicated. In this case, there is a -2, which means the graph will move down by 2.
If I am looking at another function like sin(2x), I again look what is inside the parenthesis. In this case, a number is now being multiplied by x, rather than being added/subtracted. If the number is a whole number, then the graph will be compressed horizontally. If it's a fraction, then the graph will be stretched-out. Once again, think the opposite.
2. Trigonometry
When it comes to the unit circle, I don't have a hard time remembering where everything goes. If I am trying to find the coordinates of each pi, then I just remember that the short sides are 1/2 and the long sides are 3/2. That leaves the sides that are 2/2. From there, I just insert a negative if it is necessary. If I know that, then I can find where the pi's go. For all the coordinates that have 3/2 as the x, it is _pi/3. The coordinates that have 1/2 as the x, it is _pi/6. The rest are _pi/4. It all comes to me when I see the unit circle on paper.
With graphs, I remember that cosx will always have the point (0,1) and sinx will have (0,0). I know the curves for both, so I don't have a trick to remember that. For the rest, tanx, cscx, secx, cotx, I keep in mind that all are going to have asymptotes.
3. What confuses/worries me
The inverse graphs still troubles me because I don't remember the domain and range for most of them. I sometimes forget that I am supposed to switch x and y values. That means that the range will include pi's and the domain will not.
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The inverses are tricky I know....:-s And yeah thats true sinx and cosx are the main ones for me so I know the rest will have asymptotes! :)
ReplyDeleteAHHH, i SO dont get it.. i barely grasped the whole thing about subracting x inside and outside parenthesis moving it vertically and horizontally.
ReplyDeleteso 2x is COMPRESSED?? that means a smaller period right?? meaning that 1/2x would be a longer period?? or does it affect the amplitude?? its that stuff that i still dont understand. if its multiplying or dividing x, is that the amplitude or the period that changes?