The graph of the function $$ y=f(x+65) $$ can be obtained from the graph of $$ y=f(x) $$ by one of the following actions: Oshifting the graph of $$ f(x) $$ to the left 65 units Shifting the graph of $$ f(x) $$ upwards 65 units shifting the graph of $$ f(x) $$ to the right 65 units shifting the graph of $$ f(x) $$ downwards 65 units Question Help: Video

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Consider the function transformation $$ y = f(x+65) $$.

1. In the function $$ f(x+65) $$, every occurrence of $$ x $$ is replaced by $$ x+65 $$.
2. To understand how this affects the graph, we can set $$ u = x+65 $$. Then the function becomes $$ y = f(u) $$.
3. For a given output $$ y $$, the input $$ u $$ relates to $$ x $$ by $$ x = u - 65 $$.
4. This means the graph of $$ f(x) $$ is shifted so that every $$ x $$-coordinate is decreased by 65.
5. A decrease in the $$ x $$-coordinate by 65 corresponds to a shift to the left by 65 units.

Thus, the graph of $$ y = f(x+65) $$ can be obtained from the graph of $$ y = f(x) $$ by shifting it to the left 65 units.
The graph of $$ y = f(x+65) $$ is obtained by shifting the graph of $$ y = f(x) $$ to the left by 65 units.

The graph of the function

can be obtained from the graph of

by one of the following actions:
Oshifting the graph of to the left 65 units
Shifting the graph of upwards 65 units
shifting the graph of to the right 65 units
shifting the graph of downwards 65 units
Question Help: Video

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The graph of the function can be obtained from the graph of by one of the following actions: Oshifting the graph of to the left 65 units Shifting the graph of upwards 65 units shifting the graph of to the right 65 units shifting the graph of downwards 65 units Question Help: Video