Without graphing, what is the transformation that takes place between the graph #y=1/x# and the graph of #y=1/(x+5)-2#?

1 Answer
Azimet
Jan 15, 2017

The graph of #g# is the graph of #1/x#, shifted #5# units to the left, and #2# units down.

Explanation:

Let #f(x) = 1/x#, and #g(x) = 1/(x+5) - 2#. Then,

#g(x) = f(x+ 5) - 2#.

Therefore, the graph of #g# is the graph of #f#, shifted #5# units to the left, and #2# units down.

In general, for any two functions #f,g#, if #g(x) = f(x - a) + b#, then

the graph of #g# is the graph of #f# shifted #a# units to the right, and #b# units upwards. Negative values mean opposite directions.

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