Mathematics: Ionly need with this one. can you also explain it for me and how i can solve future problems like this?

Ionly need with this one. can you also explain it

Ответ:

sylviaangelinn

10.01.2022

$\bf \qquad \qquad \qquad \qquad \textit{function transformations}
\\ \quad \\\\

\begin{array}{rllll} 
% left side templates
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}$

so hmm notice that template above, keep in mind that

$\bf \begin{array}{llll}
% right side info
\bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\
\bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}
\\\\
\bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\
\qquad if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\
\end{array}$

$\bf \begin{array}{llll}

\bullet \textit{ vertical shift by }{{ D}}\\
\qquad if\ {{ D}}\textit{ is negative, downwards}\\\\
\qquad if\ {{ D}}\textit{ is positive, upwards}\\\\
\bullet \textit{ period of }\frac{2\pi }{{{ B}}}
\end{array}$

so hmm with that in mind, let's take a peek of yours

$\bf \begin{array}{llllll}
g(x)=&(&x&-4)^2&+2\\\\
g(x)=&1(&1x&-4)^2&+2\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}$

C is -4, thus, the horizontal shift from f(x), is to the "right by 4 units", or you can use the C/B notation, will will be -4/1 or -4 anyway

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Ответ:

shamim5364

25.01.2020

Mathematics

Both ANGLE AND LINE SEGMENT are correct. Thus, the correct answers are B and D.
The postulate that describe how angle and line segment are measured are the protractor postulate [angle measure postulate] and the ruler postulate [point line plane postulate] respectively.

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Ionly need with this one.
can you also explain it for me and how i can solve future problems like this?

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