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February 7th, 2015, 04:45 AM   #1
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Function transformation issues

Hi. I have 'most' of the basic rules down but some are still throwing me i'm off. For insance i'm given a graph and asked to manipulate it and there's a few I don't understand. I obviously can post the graph but the important part is the function. I have a few questions, i'll try just asking a couple for now. Please try to make it as simple as possible i've already racked my brain on this to no avail.

1. y=f(2x).

It's my understanding that this messes with the x values? I don't understand how this is supposed to be divided by 2 and not times 2?

So if it were y=f(1/2x) then it would be 2x? Asides if this is correct i'd still like an explanation if you have one.

2. y=2f(x). This looks to be messing with the y value? It looks to make sense here to me that it would expand the y value by 2?
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February 7th, 2015, 12:45 PM   #2
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1. Step 1: choose a value for x, step 2: multiply by 2, step 3: evaluate the function at this value.

2. If you mean multiply by 2, yes.
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February 7th, 2015, 05:10 PM   #3
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From what I understand, for any x value entered, you'd be doubling the y output.

Lets look at a straight positive line. f(x)=x. Any x value you input will have an equal y output. Input a 7 for x and you get the point (7,7). Easy, no math involved really. Same for -3, which gives you the point (-3,-3), and also 0, which crosses the origin at (0,0). This probably seems obvious, but cementing this might help you understand.

Ok, so if this is true, then what happens with f(2x)? Does the 2 effect the x or the y value? Its next to the X, but its in the Y?

Lets start fresh now. For simplicity's sake, we can say that f(2x) is the same as f(x)=2x. You can still plug in any x value you want, just like before. Nothing touches that X value. You plug it in as normal, but the resultant y value is now double what it was before.

Now input 0.

You get an origin intersect just like before. f(x)=2x basically just means your stretching ALL of your Y-values by a factor of 2, from the y-axis upward and downward. If 1/2 gave you 1/2 before, now 1/2 gives you 1. Likewise an x value of 5 will give you a y value of 10.

I hope this helped!

Last edited by mth111man; February 7th, 2015 at 06:03 PM.
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