Transformation of Graphs: y=1/(x^3+3) translated by [2,1]

[Monkeyseat]

The curve y=1/(x^3 + 3) is translated by the vector [2, 1] to give the curve with equation y = f(x). Write down an expression for f(x). Do not simplify your answer.

Ok so I thought it would be:

f(x)=1/((x - 2)^3 + 3) for the shift of 2 units to the right.

Then:

f(x)=1/((x - 2)^3 + 4) for the additional shift of 1 unit upwards.

This is wrong apparently. I was told it was f(x)=1/((x - 2)^3 + 3) + 1

Why is the one added on afterwards and not to the 3?

Thanks.

 

[stapel]

The "3" is part of the original function. It was already in the denominator. Moving it out of the denominator would have changed the function.

The "1" is the vertical shift. Putting it in the denominator should not have shifted the graph, and would have changed the function.

Eliz.

 

[Monkeyseat]

Re:

The "3" is part of the original function. It was already in the denominator. Moving it out of the denominator would have changed the function.

The "1" is the vertical shift. Putting it in the denominator should not have shifted the graph, and would have changed the function.

Okay thanks - so is the (x - 2)^3 bit right? I.e. should the 2 shift to the right be on the denominator?

 

[stapel]

The left-right shift (that is, the change in x) should be in the "x" part of the function. Since the x-part is in the denominator, inside a cube, then the left-right shift belongs there, too.

To learn about function translations / transformations, try studying some of the many great lessons available online:

. . . . .Google results for "function transformation"

. . . . .Google results for "function translation"

The rules are fairly straightforward. Have fun!

Eliz.

 

[Monkeyseat]

Re:

The left-right shift (that is, the change in x) should be in the "x" part of the function. Since the x-part is in the denominator, inside a cube, then the left-right shift belongs there, too.

To learn about function translations / transformations, try studying....

Thanks!