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# if the graph of y = 1/(2x-4) +3 is transformed to y = 1/x, is it translated to the left by 4 units or 2 units?

Could you please also explain your reasoning?

### 4 Answers

- alexLv 72 years ago
Rule

y=1/x ----> 1 / (a * (x - b)) + c

dilate factor 1/a from x-axis

translate b units to the right and c units up

- RealProLv 72 years ago
OK so when doing transformations on a function there's no rule saying "first do the dilation and then translation", not that I know of at least.

I assume most people first do the dilation. But geometry doesn't break if you try it the other way.

So starting from y=1/x you can first squish the graph the horizontal direction (with respect to y-axis) by a factor of 1/2

y = 1/(2x)

Then you can translate right by two units

y = 1 / (2(x-2)) = 1 / (2x-4)

Note how "x" is exactly always replaced by "x-2" for a translation of 2 units.

BUT if you first do the translation 4 units to the right

y = 1/x ===> y = 1/(x-4)

And then you do a squish in the horizontal direction by a factor of 1/2 (which is done by dividing x with 1/2, so you get 2x)

y = 1/(2x-4)

Both processes result in the same function. Translation of 4 units to the right is if you do it before the dilation and 2 units is if you do the dilation first.

- 2 years ago
By 2 units

1 / (2x - 4) + 3 =>

1 / (2 * (x - 2)) + 3

Your goal is to get the x in the denominator to have a coefficient of 1 in its expression

y = 1 / x

Is really

1 / (a * (x - b)) + c

It's just that when we have 1/x, that means that a = 1 , b = 0 and c = 0.