How do we shift the graph of $$ y=g(x) $$ to get the graph of $$ y=g(x+5) $$ ?

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1. Recognize that in the transformation $$ g(x+5) $$, the expression inside the function has the form $$ x+5 $$.

2. For a horizontal shift, replacing $$ x $$ with $$ x+5 $$ shifts the graph to the left by 5 units (since adding a positive constant inside $$ g(\cdot) $$ moves the graph in the negative $$ x $$-direction).

3. Thus, the graph of $$ y=g(x+5) $$ is obtained by shifting the graph of $$ y=g(x) $$ 5 units to the left.
To shift the graph of $$ y=g(x) $$ to the graph of $$ y=g(x+5) $$, move the original graph 5 units to the left.

How do we shift the graph of to get the graph of ?

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