How to describe the stretches on the x-axis

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bigmansouf
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I was tackling the solomon worksheets and I noticed a potential mistake I had when describing the stretches on the x-axis
The link to the solomon worksheet for Graph of functions is here
http://pmt.physicsandmathstutor.com/...0Questions.pdf

The problem I have is Worksheet B question 10
But asked to describe the transformation of worksheet B Question 10
I wrote; a stretched by a factor of 3 in the x-direction but the worksheet gave a different answer link: http://pmt.physicsandmathstutor.com/...%20Answers.pdf



for worksheet B Question 10
I thought that to transform  y=f(x)= \frac{1}{x} to  y = \frac{1}{3x} you can perform a stretch by a factor 3 in the x-direction
 y = f(\frac{1}{3}x)  which stretches the graph by a scale factor of 1/a
therefore 1\a becomes  \frac{1}{\frac{1}{3}} = 3
as a result the graph y =f(x) is stretch to  y = f(\frac{1}{3}x) = \frac{1}{3x}


Am i right and the answer given wrong?
Also I think a similar mistake is done for Worksheet B question 6C

Please share your thoughts

Thank you
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Philip-flop
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(Original post by bigmansouf)
I was tackling the solomon worksheets and I noticed a potential mistake I had when describing the stretches on the x-axis
The link to the solomon worksheet for Graph of functions is here
http://pmt.physicsandmathstutor.com/...0Questions.pdf

The problem I have is Worksheet B question 10
But asked to describe the transformation of worksheet B Question 10
I wrote; a stretched by a factor of 3 in the x-direction but the worksheet gave a different answer link: http://pmt.physicsandmathstutor.com/...%20Answers.pdf



for worksheet B Question 10
I thought that to transform  y=f(x)= \frac{1}{x} to  y = \frac{1}{3x} you can perform a stretch by a factor 3 in the x-direction
 y = f(\frac{1}{3}x)  which stretches the graph by a scale factor of 1/a
therefore 1\a becomes  \frac{1}{\frac{1}{3}} = 3
as a result the graph y =f(x) is stretch to  y = f(\frac{1}{3}x) = \frac{1}{3x}


Am i right and the answer given wrong?
Also I think a similar mistake is done for Worksheet B question 6C

Please share your thoughts

Thank you
I haven't read the actual question but...

If  f(x) = \frac{1}{x} then  f(3x) = \frac{1}{3x} which means it is a stretch parallel to the x axis of  \frac{1}{3}
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plaguarist
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Not quite right. The x is on the bottom. Imagine it as 1/ (x) then to get the desired function it must have been either f(3x) or (1/3)f(x)

Both give a stretch of scale factor 1/3.
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RDKGames
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(Original post by bigmansouf)
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If f(x)=\frac{1}{x} then f(3x)=\frac{1}{3x} which is a stretch in the x-axis by a scale factor of 1/3.

If it were a stretch sf 3 then you would have f(\frac{1}{3}x)=\frac{1}{\frac{1}{3}x}=\frac{3}{x} which isn't the same.

Alternatively, consider \displaystyle \frac{1}{3}f(x)=\frac{\frac{1}{3}}{x}=\frac{1}{3x} which is a stretch parallel y-axis by sf 1/3.
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