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

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Answer 1 · 2017-01-15T18:04:23

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

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.

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