Question

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

Answer 1

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.

Answer 2

that didn't help me

Answer 3

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.

Answer 4

ok

Answer 5

You didn't write the transformed equation correctly, I think. Isn't it
\[g(x) = -(2)3^{x-1} + 2\]
?

Answer 6

so since its a positive its 2 unit up right

Answer 7

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.

Answer 8

I wrote it right

Answer 9

Is the -1 part of the exponent, or not?

Answer 10

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.

Answer 11

yes and ok

Answer 12

forget it I will figure it out

Answer 13

so if writing it on a single line as you did, you would need to write g(x) = (-2)3^(x-1) + 2

Answer 14

Are you interested in learning this material, or not?

Answer 15

yes I am

Answer 16

your a troller

Answer 17

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!

Answer 18

lol

Answer 19

so the transformation that is not applied is 2 units down

Answer 20

Yes.

Answer 21

soo was I right

Answer 22

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.

Answer 23

ok

Answer 24

ok can you be specific

Answer 25

About what?

Answer 26

Sorry, the - sign in front of the "- 2" at the right end of the equation...

Answer 27

Problem writer probably used the 2 in different places just to confuse you :-)

Answer 28

oooo

Answer 29

is that what you wanted me to be more specific about?

Answer 30

I guess

Answer 31

Well, tell me what you want, and I'll try to give it to you. I can't read your mind...

Answer 32

the answer in a explained way please

Answer 33

^because I have another problem like this and I want to figure it out

Answer 34

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...

Answer 35

Post the other question and I'll check your work on it...

Answer 36

ok