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1) The region between the graph of $y = f (x)$ and the $x$-axis, shaded in this figure, has an area of 10 square units. What is the area between the graph of $y = \dfrac 12 f (-x)$ and the $x$-axis?

 

 

2) The region between the graph of $y = f (x)$ and the $x$-axis, shaded in this figure, has an area of 10 square units. What is the area between the graph of $y = \dfrac 12 f (-x)$ and the $x$-axis?

 

 Sep 27, 2022
 #1
avatar+1005 
+2

Lol this is AoPS algebra 2 math homework... I will not say the answer, but I will be saying a hint. 1/2 is halving the height of the object, and reflecting across the y axis won't do anything... Thus use geometry. 

 Sep 27, 2022
 #2
avatar+118132 
+2

Hi Proyaop

Why do you think that this function is even. It does not say so in the question.

How can you know what   f(-x) looks like at all?

 Sep 27, 2022
 #7
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lol i saw this question before i forgot the answer but all i remember was that the answer was super uber uber uber obvious lololol

Guest Oct 5, 2022
 #3
avatar+588 
+2

Im not sure what that is, but this is school homework I got. So help would be appreciated

 Sep 30, 2022
 #5
avatar+588 
+1

For number 1 the question is: The region between the graph of y=f(x) and the x-axis, shaded in this figure, has an area of 10 square units. What is the area between the graph of y=f(x+2) and the x-axis?

 

And yes the negative sign is in the correct place for number 2

 Oct 5, 2022
 #6
avatar+1005 
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The function is in the image (the part w/o the shaded region)... So if you were to compress that that would be taking half the gray region right?

 Oct 5, 2022
edited by proyaop  Oct 5, 2022
 #8
avatar+1005 
+2

Hey weredumbmaster22: I found the original post to this question, here it is:

https://web2.0calc.com/questions/i-m-stuck-on-these

 Oct 5, 2022
 #9
avatar+118132 
0

Thanks proyaop for finding that answer.

 

This was a great question and the answer by Oofrence was really good.

 

https://web2.0calc.com/questions/i-m-stuck-on-these#r3

Melody  Oct 12, 2022

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