What is the equation of the function y = 2/x translated 3 units to the left and 4 units up?

Solution:

To translate the function y = 2/x to the left, the denominator is modified from x to x +3 i.e.

y = 2/( x + 3)

The translation below shows the shift to the left in the graph as:

translaion of graph y = 2/x

To shift the function ‘up’ we add 4 to the function and the function y = 2/x will look like

y = (2/x) + 4

and graph will shift up as shown below:

y = 2/x + 4

The combined effect of shifting left and moving up is shown in the final graph below:

y = (2/(x + 3)) + 4

What is the equation of the function y = 2/x translated 3 units to the left and 4 units up?

Summary:

The equation of the function y = 2/x translated 3 units to the left and 4 units up is y = (2/(x + 3)) + 4

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