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Mathematics

2 answers:

EastWind [94]3 years ago

7 0

<h2>My discord username is !!#7467, and if you play roblocs my username is angeliqcore! <3</h2>

vovikov84 [41]3 years ago

7 0

my discord is EnderGaming IO#4909

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How does the graph of f(x) =-3^2x-4 differ from the graph of g(x)=-3^2x

Neko [114]

$\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
% templates
f(x)={{ A}}({{ B}}x+{{ C}})+{{ D}}
\\\\
~~~~y={{ A}}({{ B}}x+{{ C}})+{{ D}}
\\\\
f(x)={{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\\\
f(x)={{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\\\
f(x)={{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\\\\
--------------------$

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

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

with that template in mind, let's check,

$\bf f(x)=-3^{\stackrel{B}{2}x\stackrel{C}{-4}}\qquad \qquad g(x)=-3^{2x}\implies g(x)=-3^{\stackrel{B}{2}x\stackrel{C}{+0}}$

notice, g(x) has a horizontal shift of C/B or +0/2, or just 0, none.

while f(x) has a horizontal shift of C/B or -4/2, or -2, to the right.

so f(x) is really just g(x), but shifted horizontally over 2 units to the right.

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