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Mathematics
23.05.2022 13:15
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What effect does changing the function g(x)=logx to f(x)=log(x+3)+2 have on the

What effect does changing the function g(x)=logx to f(x)=log(x+3)+2 have on the graph of g(x)?
the graph shifts 3 units to the left and 2 units up.
the graph shifts 3 units to the right and 2 units down.
the graph shifts 2 units to the right and 3 units down.
the graph shifts 2 units to the left and 3 units up.
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culbertchristi5634
culbertchristi5634
4,9(82 marks)
\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}}\\\\
f(x)=&{{ A}} log\left({{ B }}x+{{ C}} \right)+{{ D}}
\end{array}\qquad

\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}

with that template in mind, let's see

\bf \begin{array}{lllcclll}
f(x)=&1log(&1x&+3)&+2\\
&\uparrow &\uparrow &\uparrow &\uparrow \\
&A&B&C&D
\end{array}
\\\\\\
\textit{horizontal shift by }\cfrac{C}{B}\implies \cfrac{3}{1}\implies +3\textit{ units to the left}
\\\\\\
\textit{vertical shift by }D=+2\textit{ units upwards}
triddi666
triddi666
4,4(22 marks)

Spending total: $18.25

Change given back: $1.74

Step-by-step explanation:

$3.25+$11.00+$4.00=$18.25

$20.00-$18.25=$1.75

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