Can anyone help me solve these?

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Ad2. I actually don't know how to do the second one properly. I only know that I have to make g(x)=|f(x)| but still don't know if the first step is right. Could anyone give me some hints on how to even start that?
Ad1. About the first one, I know that g(-3) makes that x=-3 but don't know what to do afterwards. Should I multiply every x by -3? It would be really nice if you helped me ! My teacher genuinely didn't say a word on how to do these exercises.
 
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And here, it will make it easier to read:
  1. State which combination of transformations has been applied to f(x)=(x-2)^2 + 1 to get g(x)=|(2x+1)^2 -5|
  2. Let g(x)=2f(x+3) -2 Find g(-3)
 
En4rgy said:
And here, it will make it easier to read:
  1. State which combination of transformations has been applied to f(x)=(x-2)^2 + 1 to get g(x)=|(2x+1)^2 -5|
  2. Let g(x)=2f(x+3) -2 Find g(-3)
Click to expand...
Where is work and where are you stuck?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
Subhotosh Khan said:
Where is work and where are you stuck?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
Click to expand...
I shared my thoughts and my work in the first reply. I need some hints to continue. And about the second exercise, i truly don't know how to even start properly. I only suspect as there is absolute value you have to apply that to this function : g(x)=|f(x)| but i don't know where to go afterwards.
 
En4rgy said:
I shared my thoughts and my work in the first reply. I need some hints to continue. And about the second exercise, i truly don't know how to even start properly. I only suspect as there is absolute value you have to apply that to this function : g(x)=|f(x)| but i don't know where to go afterwards.
Click to expand...
If I were to do #1, I would plot f(x) and g(x) on a graph paper and observe what I can gather.
 
I think i have done the first one
g(-3)= 2f(-3 +3) -2
g(-3) = -2
Although i am not sure about this one
Btw. im sorry for responding late but i had to eat something
 
Subhotosh Khan said:
If I were to do #1, I would plot f(x) and g(x) on a graph paper and observe what I can gather.
Click to expand...
And about the 1 a) I actually know how to do it.
1. Reflection in the x-axis.
2. Translation by 3 units up.
And sketching is easy
 
Ok i thought about the second exercise and thats what i came up with:
1.g(x)=|f(x2)|
2.g(x)=f(2*x)2
3.g(x)=f(2x+3)2 - 6
 
En4rgy said:
And here, it will make it easier to read:
  1. State which combination of transformations has been applied to f(x)=(x-2)^2 + 1 to get g(x)=|(2x+1)^2 -5|
  2. Let g(x)=2f(x+3) -2 Find g(-3)
Click to expand...
g(-3) = 2f(-3+3) - 2 = 2f(0) - 2 =....
 
f(x)=(x-2)^2 + 1 to get g(x)=|(2x+1)^2 -5| Define G(x) = (2x+1)^2 -5

What is the horizontal shift from f to G? What is the vertical shift from f to G?

If you prefer you can add another function, say h(x), where h(x) = x^2

How do you go from h to f and from h to G? With those results known how do you go from f to G?

Now how do you go from G to g? From f to G?
 
Jomo said:
f(x)=(x-2)^2 + 1 to get g(x)=|(2x+1)^2 -5| Define G(x) = (2x+1)^2 -5

What is the horizontal shift from f to G? What is the vertical shift from f to G?

If you prefer you can add another function, say h(x), where h(x) = x^2

How do you go from h to f and from h to G? With those results known how do you go from f to G?

Now how do you go from G to g? From f to G?
Click to expand...
1. There is horizontal translation by 3 to left and vertical translation 6 down. There is a dilation on x-axis with the scale factor 1/2 as well i think? Am i getting it right?
 
En4rgy said:
Is it g(-3)= -2 ?
I'm sorry for lack of my knowledge...
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It does not see to be -2. I need to see the graph or know the function f(x). Based on the portion of the graph I do see, it seems that f(0) is a bit above -2 but clearly negative. If you multiple a negative number by 2 it will certainly get more negative. Now if then subtract 2 from that negative number you will get a number less than -2 which can't be -2.
 
En4rgy said:
1. There is horizontal translation by 3 to left and vertical translation 6 down. There is a dilation on x-axis with the scale factor 1/2 as well i think? Am i getting it right?
Click to expand...
I would not know if you are getting it correct or not. Since I introduced other functions, like G and h, I am not sure between which two functions you listed your transformation for.
 
Jomo said:
I would not know if you are getting it correct or not. Since I introduced other functions, like G and h, I am not sure between which two functions you listed your transformation for.
Click to expand...
Those transformations are from f to g
 
1st of all, f and g do not look the same (because of the absolute value part. That means that you can not go from f to g by just translations.

How do you go from f to G? That is your first concern. The values you listed for the horizontal is not correct.
 
From f to G:
1. Horizontal translation by 3 to the right, Vertical Translation by 6 up.
And the dialation on x-axis with scale factor 1/2
 
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