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

Sep 30, 2022
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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
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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
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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
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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