Translations

[noahstaz]

My question is with number 3 c

I was wondering why the answer for the horizontal translation is one right, rather than one left like 3a. I have a feeling it has to do with absolute value, but Id like to know a full reason why for my midterm exam tomorrow.

Thanks!

 

[Dr.Peterson]

My question is with number 3 c

I was wondering why the answer for the horizontal translation is one right, rather than one left like 3a. I have a feeling it has to do with absolute value, but Id like to know a full reason why for my midterm exam tomorrow.

Rewrite |-x+1|+3 as |-(x-1)|+3, and then, optionally, as |x-1|+3. I suspect they will not have done the last step, as that depends on a property of the original function.

In general, a factored form like -(x-1) displays the transformation better than the unfactored form, -x+1. So while the absolute value can play a role (because of its symmetry, which allows you to ignore the reflection, if you wish), it is the ax+b form as opposed to a(x+b) that changes the direction of the translation.

If you show me the provide answer, I may have more to say.