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inessss [21]
3 years ago
9

How can you use transformations to graph this function? y=3x

xFormula1" title=" 7^{-x} " alt=" 7^{-x} " align="absmiddle" class="latex-formula">+2
Mathematics
1 answer:
dimulka [17.4K]3 years ago
7 0
\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
y=&{{  A}}({{  B}}x+{{  C}})+{{  D}}
\\ \quad \\
f(x)=&{{  A}}\sqrt{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}}(\mathbb{R})^{{{  B}}x+{{  C}}}+{{  D}}
\\ \quad \\
f(x)=&{{  A}} sin\left({{ B }}x+{{  C}}  \right)+{{  D}}
\end{array}\\\\
--------------------

\bf \bullet \textit{ stretches or shrinks horizontally by  } {{  A}}\cdot {{  B}}\\\\
\bullet \textit{ flips it upside-down if }{{  A}}\textit{ is negative}\\
\left. \qquad   \right.  \textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if }{{  B}}\textit{ is negative}\\
\left. \qquad   \right.  \textit{reflection over the y-axis}

\bf \bullet \textit{ horizontal shift by }\frac{{{  C}}}{{{  B}}}\\
\left. \qquad  \right. if\ \frac{{{  C}}}{{{  B}}}\textit{ is negative, to the right}\\\\
\left. \qquad  \right.  if\ \frac{{{  C}}}{{{  B}}}\textit{ is positive, to the left}\\\\
\bullet \textit{ vertical shift by }{{  D}}\\
\left. \qquad  \right. if\ {{  D}}\textit{ is negative, downwards}\\\\
\left. \qquad  \right. if\ {{  D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{  B}}}

with that template in mind, let's check

\bf y=\stackrel{A}{3}(7^{\stackrel{B}{-1}x})\stackrel{D}{+2}    <---- so the parent function will then be y = 7⁻ˣ

A = 3    it shrinks, in relation the y-axis, by a factor of 3 times, so is narrower.

B=-1     well, it flips it sideways, reflection over the y-axis.

D= +2  well, that's just a vertical shift of 2 units.
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A positive slope means this line rises

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Slope: m=\frac{3-2}{5--1}=+\frac{1}{6}

A positive slope means this line rises

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A zero slope means the line is horizontal

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Slope: m=\frac{\frac{1}{4}-\frac{1}{2}}{5-4}=-\frac{1}{4}

A negative slope means this line falls.

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<u />

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