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$($a$)$ If $c>0,$ the graph of $y=f(x)+c$ is obtained by shifting the graph of $y=f(x)$ to the a distance of $c$ units. The graph of $y=f(x)-c$ is obtained by shifting the graph of $y=f(x)$ to the a distance of $c$ units.

$($b$)$ If $c>0,$ the graph of $y=f(x)-c$ is obtained by shifting the graph of $y=f(x)$ to the a distance of $c$ units. The graph of $y=f(x)+c$ is obtained by shifting the graph of $y=f(x)$ to the a distance of $c$ units.