C3 successive transformations HELP! Watch

TMCkins
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Hey all, got abit of a problem with this transformation question! It says, the graph of y=x^3 is enlarged by a factor of 2 in both the x- and y-directions. Give there new equations.
I was going along the lines of y=2(x^3) for the y- enlargement and then y= 2(x^3/2) to include the x- enlargement, but this will just cancel out...

The correct answer is 4y=x^3

Any help would be great!
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Indeterminate
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(Original post by TMCkins)
Hey all, got abit of a problem with this transformation question! It says, the graph of y=x^3 is enlarged by a factor of 2 in both the x- and y-directions. Give there new equations.
I was going along the lines of y=2(x^3) for the y- enlargement and then y= 2(x^3/2) to include the x- enlargement, but this will just cancel out...

The correct answer is 4y=x^3

Any help would be great!
Well, let

y= f(x) = x^3

Noting that the x to which f is applied on the LHS relates to each x in the RHS, so f(m) = m^3 for x=m

Now note that

f(ax) is a stretch by scale factor \frac{1}{a} in the x direction.

Similarly

bf(x) is a stretch by scale factor b in the y-direction.

What are a and b in your case?
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TenOfThem
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(Original post by TMCkins)
Hey all, got abit of a problem with this transformation question! It says, the graph of y=x^3 is enlarged by a factor of 2 in both the x- and y-directions. Give there new equations.
I was going along the lines of y=2(x^3) for the y- enlargement and then y= 2(x^3/2) to include the x- enlargement, but this will just cancel out...

The correct answer is 4y=x^3

Any help would be great!
The dividing by 2 has to be x/2 before you cube it
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TheSK00T3R
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Tranformation rules:
y=af(x) - stretch parallel to y axis scale factor a
y=f(ax) - stretch parallel to x axis scale factor 1/a

Try putting the x in brackets along with a, and the power outside the brackets.
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TMCkins
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(Original post by TheSK00T3R)
Tranformation rules:
y=af(x) - stretch parallel to y axis scale factor a
y=f(ax) - stretch parallel to x axis scale factor 1/a

Try putting the x in brackets along with a, and the power outside the brackets.
Ah, i get ya, so y=(x/2)^3
y=x^3/8
then the y-stretch
y=2x^3/8 which cancels to y=x^3/4 which is 4y=x^3
Thanks!
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