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Finding the transformation of a linear function $f(x)=mx+c$ to $f(x+a)$.

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If $f(x)=\\simplify{{m}x+{c}}$, what is $\\simplify{f(x+{a})}$?

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To make the transformation from $f(x)=\\simplify{{m}x+{c}}$ to $\\simplify{f(x+{a})}$, we want to replace the $x$-terms in $f(x)$ with $\\simplify{x+{a}}$:

\n

\\[ \\begin{split} \\simplify{f(x+{a})} &\\,= \\simplify{{m}(x+{a})+{c}} \\\\ &\\,= \\simplify[!collectNumbers]{{m}x+{m*a}+{c}} \\\\ &\\,= \\simplify{{m}x+{m*a+c}}. \\end{split} \\]

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$\\simplify{f(x+{a})}=$[[0]]

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