How domain and range changes when a function is transformed ...

[babymathteacher]

Hi all,

I am having trouble with the following question:



I thought I was getting it: the vertical transformations would affect the range and the horizontal transformations would affect the domain. I got to c) and it was waaaay off so I am assuming my technique isn't useful in the long run. Could someone show me using c) how to find the "updated" domain and range?

Thank you in advance,
babymathteacher ◡̈

 

[stapel]

Hi all,

I am having trouble with the following question:

View attachment 35809

I thought I was getting it: the vertical transformations would affect the range and the horizontal transformations would affect the domain. I got to c) and it was waaaay off so I am assuming my technique isn't useful in the long run. Could someone show me using c) how to find the "updated" domain and range?

Please reply with a clear listing of the steps you took, the result you obtained, and the "correct" answer expected (which might itself be in error).

Thank you!

Eliz.

 

[babymathteacher]

Hi,

Here was what I attempted:



Here is what the solutions say:



Here is what I found online when looking for an explanation but it doesn’t explain much:



Best,

babymathteacher

 

[Dr.Peterson]

Please show the details here:



How did you get from $x\ge-4$ to $x\le-3$ by shifting one unit left? And why did you write "D+1"?

Your general ideas are all correct; you just have to carry them out carefully.

But their answers are not quite right, either; they changed $\ge$ to $>$:

 

[blamocur]

Hi all,

I am having trouble with the following question:

View attachment 35809

I thought I was getting it: the vertical transformations would affect the range and the horizontal transformations would affect the domain. I got to c) and it was waaaay off so I am assuming my technique isn't useful in the long run. Could someone show me using c) how to find the "updated" domain and range?

Thank you in advance,
babymathteacher ◡̈

Not sure about horizontal and vertical transformations, but if $f(x)$ is defined for $x \geq -4$ then $f(x+1)$ is defined for $x+1 > -4$.

 

[babymathteacher]

Thank you all - I was doing it correctly, just making silly mistakes!

- babymathteacher