lemme post a quick template of some help
[tex]\bf ~~~~~~~~~~~~\textit{function transformations}
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% templates
f(x)= A( Bx+ C)+ D
\\\\
~~~~y= A( Bx+ C)+ D
\\\\
f(x)= A\sqrt{ Bx+ C}+ D
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f(x)= A(\mathbb{R})^{ Bx+ C}+ D
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f(x)= A sin\left( B x+ C \right)+ D
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--------------------[/tex]
[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\
\bullet \textit{ flips it upside-down if } A\textit{ is negative}\\
~~~~~~\textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if } B\textit{ is negative}[/tex]
[tex]\bf ~~~~~~\textit{reflection over the y-axis}
\\\\
\bullet \textit{ horizontal shift by }\frac{ C}{ B}\\
~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the right}\\\\
~~~~~~if\ \frac{ C}{ B}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by } D\\
~~~~~~if\ D\textit{ is negative, downwards}\\\\
~~~~~~if\ D\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{ B}[/tex]
so f(x) - k, is simply appending a constant "k", and thus is a vertical shift by k units.
f(x+h) is changing whatever "x" was to "x+h", and therefore is shifting the function to the left by h units.
f(x-h), is about the same as before, but is doing a horizontal shift to the right by h units.
