How does the graph of $f (x) = {log}_{2} (x - 5) - 2$ $f(x) = log_2(x - 5) - 2$ compare to its parent function f(x) = ${log}_{2} x$ $log_2 x$ ?

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How does the graph of $f (x) = {log}_{2} (x - 5) - 2$ $f(x) = log_2(x - 5) - 2$ compare to its parent function f(x) = ${log}_{2} x$ $log_2 x$ ?

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Answer 1 · 2015-09-07T13:09:57

${log}_{2} (x - 5) - 2$ $log_2(x-5)-2$ is ${log}_{2} (x)$ $log_2(x)$ shifted down $2$ $2$ units, and shifted right $5$ $5$ units.

Explanation:

For any function $f (x)$ $f(x)$ :

$f (x) + k$ $f(x) + k$ is $f (x)$ $f(x)$ shifted up by $k$ $k$ units.

$f (x) - k$ $f(x) - k$ is $f (x)$ $f(x)$ shifted down by $k$ $k$ units.

$f (x + k)$ $f(x+k)$ is $f (x)$ $f(x)$ shifted left by $k$ $k$ units.

$f (x - k)$ $f(x-k)$ is $f (x)$ $f(x)$ shifted right by $k$ $k$ units.

From this we can quickly see that ${log}_{2} (x - 5) - 2$ $log_2(x-5)-2$ is ${log}_{2} (x)$ $log_2(x)$ shifted down $2$ $2$ units, and shifted right $5$ $5$ units.

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How does the graph of $f (x) = {log}_{2} (x - 5) - 2$ $f(x) = log_2(x - 5) - 2$ compare to its parent function f(x) = ${log}_{2} x$ $log_2 x$ ?

1 Answer

Explanation:

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How does the graph of f(x) = log_2(x - 5) - 2f(x)=log2(x−5)−2f(x) = log_2(x - 5) - 2 compare to its parent function f(x) = log_2 xlog2xlog_2 x?

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How does the graph of $f (x) = {log}_{2} (x - 5) - 2$ $f(x) = log_2(x - 5) - 2$ compare to its parent function f(x) = ${log}_{2} x$ $log_2 x$ ?