anonymous
  • anonymous
To obtain the graph of g(x) = -(2)3^x-1 + 2 from the graph of f(x) = 3^x, which transformation is NOT applied? Answer Reflection in the x-axis. Vertical stretch by a factor of 2. Translation one unit right. Translation two units down
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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whpalmer4
  • whpalmer4
Let's go through what all of those transformations mean. Then you can make your selection of the one that is not applied. Translation two units down: this means we subtract 2 from the result of the function. A translation up would be adding to the result of the function. Translation 1 unit right: we subtract 1 from the input to the function. If we have the line \(y = x\), which is a line going through the origin (0,0) at a 45 degree angle, changing it to \(y = x-1\) shifts it 1 units to the right. Vertical stretch by a factor of 2: we multiply the result of the function by 2. For example, \(y = 2\sin x\) goes from -2 to 2 for its peak values instead of the -1 to 1 that \(y = \sin x\) does. Reflection in the x-axis: we multiply the result of the function by -1. For example, \(y = x^2\) is a parabola that opens up, but \(y = -x^2\) is the same parabola, opening down.
anonymous
  • anonymous
that didn't help me
whpalmer4
  • whpalmer4
you were hoping I would just tell you the answer, perhaps? If you look at each of those transformations, and the transformed equation, you should be able to spot whether or not any given transformation has been applied. For example, the reflection in the x-axis would cause the result of the function to be multiplied by a negative number. If that's true in the transformed equation, then the reflection is one of the transformations applied.

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anonymous
  • anonymous
ok
whpalmer4
  • whpalmer4
You didn't write the transformed equation correctly, I think. Isn't it \[g(x) = -(2)3^{x-1} + 2\] ?
anonymous
  • anonymous
so since its a positive its 2 unit up right
whpalmer4
  • whpalmer4
That's not the same as \[g(x) = -(2)3^x-1+2\]which is how what you wrote is correctly interpreted, given the order of precedence of operations.
anonymous
  • anonymous
I wrote it right
whpalmer4
  • whpalmer4
Is the -1 part of the exponent, or not?
whpalmer4
  • whpalmer4
if it is, you need parentheses around it, because exponentiation has a higher precedence than addition. And it is, because that's the only way that the translation one unit right can be part of the answer.
anonymous
  • anonymous
yes and ok
anonymous
  • anonymous
forget it I will figure it out
whpalmer4
  • whpalmer4
so if writing it on a single line as you did, you would need to write g(x) = (-2)3^(x-1) + 2
whpalmer4
  • whpalmer4
Are you interested in learning this material, or not?
anonymous
  • anonymous
yes I am
anonymous
  • anonymous
your a troller
whpalmer4
  • whpalmer4
okay, then let's skip the attitude, okay? So, we'll take the original function, and apply the various transformations and see what results. \[f(x) = 3^x\] If we apply the reflection in the x-axis, we multiply the result of the function by -1. \[-1*3^x = -3^x\] Note that this is different from (-3)^x!
anonymous
  • anonymous
lol
anonymous
  • anonymous
so the transformation that is not applied is 2 units down
whpalmer4
  • whpalmer4
Yes.
anonymous
  • anonymous
soo was I right
whpalmer4
  • whpalmer4
Vertical stretch gets you \[y=-(2)3^{x}\]Moving 1 unit right gets you \[y=-(2)3^{x-1}\]Translating down would get you \[y=-(2)3^{x-1}-2\]And that sign in front of the 2 is the only difference, so that is the transformation not applied.
anonymous
  • anonymous
ok
anonymous
  • anonymous
ok can you be specific
whpalmer4
  • whpalmer4
About what?
whpalmer4
  • whpalmer4
Sorry, the - sign in front of the "- 2" at the right end of the equation...
whpalmer4
  • whpalmer4
Problem writer probably used the 2 in different places just to confuse you :-)
anonymous
  • anonymous
oooo
whpalmer4
  • whpalmer4
is that what you wanted me to be more specific about?
anonymous
  • anonymous
I guess
whpalmer4
  • whpalmer4
Well, tell me what you want, and I'll try to give it to you. I can't read your mind...
anonymous
  • anonymous
the answer in a explained way please
anonymous
  • anonymous
^because I have another problem like this and I want to figure it out
whpalmer4
  • whpalmer4
Okay, we've got our initial function f(x). We've got a menu of 4 transformations. We've got a transformed function g(x) which incorporates 3 of those 4 transformations. We apply all 4 transformations to f(x), and compare the result with g(x) — the part that doesn't match is the transformation that wasn't applied. It's like you start out with a plain piece of paper, and you're told to cut off one corner, paint the bottom half green, cut a hole in the middle, and fold it in half. Then you compare it with the paper they show you, and observe that theirs looks just like yours, except it is purple on the bottom. That's how you decide that the "paint the bottom half green" transformation is the one that wasn't applied...
whpalmer4
  • whpalmer4
Post the other question and I'll check your work on it...
anonymous
  • anonymous
ok

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