Question

Below is an equation along with how many units and what direction the graph of the given equation is to be shifted. Give an equation for the shifted graph. Then sketch the original and shifted graphs together. y= 1/x

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Up 1 unit, right 2 units The equation is (Type an equation.)

Answer 1

y = 1/(x -2) +1

Explanation:

You want the equation and graph of y = 1/x after it has been shifted right 2 units and up 1 unit.

Translation

The graph of a function is translated right h units and up k units by ...

g(x) = f(x -h) +k

You want the function f(x) = 1/x translated with (h, k) = (2, 1). That will be ...

g(x) = f(x -2) +1

Your equation is ...

y = 1/(x -2) +1

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Additional comment

If you like, you can simplify this to ...

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

The shifted graph is shown in blue. The asymptotes of the original are the axes. The asymptotes of the shifted function are the dashed orange lines.

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