Mathematics: The graph of g(x) is the graph of f(x)=8x+20 stretched horizontally by a factor of 4. which equation describes the function g? 1. g(x)= 8x+52. g(x)= 2x+53. g(x)= 32x+204. g(x)= 2x+20

i isStep-by-step explanation:confuzled...

The graph of g(x) is the graph of f(x)=8x+20 stretched

Ответ:

cofran

13.03.2022

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\
% left side templates
\begin{array}{llll}
f(x)=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
y=&{{ A}}({{ B}}x+{{ C}})+{{ D}}
\\ \quad \\
f(x)=&{{ A}}\sqrt{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}}(\mathbb{R})^{{{ B}}x+{{ C}}}+{{ D}}
\\ \quad \\
f(x)=&{{ A}} sin\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\\\\
--------------------$

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

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

f(x)=8x+20 is just a linear function, to have it "widen horizontally", that means the A component is some amount less than 1.

to expand it 4 times as much as the parent y = x, then

A = 1/4

$\bf f(x)=\stackrel{A}{\cfrac{1}{4}}(\stackrel{B}{8}x\stackrel{C}{+0})\stackrel{D}{+20}\implies f(x)=\cfrac{1}{4}(8x)+20\implies f(x)=2x+20$

graph it if you wish.

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The graph of g(x) is the graph of f(x)=8x+20 stretched horizontally by a factor of 4. which equation describes the function g? 1. g(x)= 8x+52. g(x)= 2x+53. g(x)= 32x+204. g(x)= 2x+20

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