drawing graph for transformed equation Watch

Henny987
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y=4/x-6 plus 5

What are the intercepts and assymptotes?
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Shaanv
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Let f(x)=1/x. f(x-6)=1/(x-6). This transformation shifts the graph 6 units to the right.
4f(x-6)=4/(x-6). This corresponds to a vertical stretch on the previous graph of scale factor 4.
4f(x-6) 5=4/(x-6) 5. This means that we translate the previous graph 5 units upwards.

If u consider the asymptotes of f(x) and how the graph changes as a result of each transformation happening one after the other, u should be able to follow through and obtain values for the asymptotes.

Alternatively u could let x tend towards infinity, and make the denominator of the fraction equal zero.
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Henny987
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(Original post by Shaanv)
Let f(x)=1/x. f(x-6)=1/(x-6). This transformation shifts the graph 6 units to the right.
4f(x-6)=4/(x-6). This corresponds to a vertical stretch on the previous graph of scale factor 4.
4f(x-6)+5=4/(x-6) + 5. This means that we translate the previous graph 5 units upwards.

If u consider the asymptotes of f(x) and how the graph changes as a result of each transformation happening one after the other, u should be able to follow through and obtain values for the asymptotes.

Alternatively u could let x tend towards infinity, and let x tend towards 6 from above and below and find the values that the function approaches but never reaches.
so are the assymptotes the same as the x and y interceptions
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Shaanv
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(Original post by Mark jam)
so are the assymptotes the same as the x and y interceptions
Nope, the asymptotes are what the graph approaches but never reaches.

Hold on a second im gonna try making a visual aid to help u figure out what is happening.
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Shaanv
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[link]https://www.desmos.com/calculator/ndam8u3fdu[/link]

Follow the graphs and how the asymptotes change with each individual transformation as i described above.
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Henny987
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Ok thanks i understand!
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RDKGames
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(Original post by Shaanv)
Nope, the asymptotes are what the graph approaches but never reaches.
It can definitely reach it, ie \dfrac{x-1}{x^2} intersects its own horizontal asymptote, so just a better choice of words is required.
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Shaanv
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(Original post by RDKGames)
It can definitely reach it, ie \dfrac{x-1}{x^2} intersects its own horizontal asymptote, so just a better choice of words is required.
Oh my bad. How would you word it?
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RDKGames
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(Original post by Shaanv)
Oh my bad. How would you word it?
An asymptote is a certain line which the graph of our function approaches as it tends to plus/minus infinity
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