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zalisa [80]
2 years ago
15

Write a formula for the function g(x) obtained when the graph of f(x)= square root x is shifted up 1 unit and to the left 9 unit

s .
Mathematics
1 answer:
ch4aika [34]2 years ago
4 0

\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
f(x)= A( Bx+ C)+ D
\\\\
~~~~y= A( Bx+ C)+ D
\\\\
f(x)= A\sqrt{ Bx+ C}+ D
\\\\
f(x)= A(\mathbb{R})^{ Bx+ C}+ D
\\\\
f(x)= A sin\left( B x+ C \right)+ D
\\\\[-0.35em]
~\dotfill\\\\
\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}


\bf ~~~~~~\textit{reflection over the y-axis}
\\\\
\bullet \textit{ horizontal shift by }\frac{ C}{ B}\\
~~~~~~if\ \frac{ C}{ B}\textit{ is negative, to the 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 take a peek.


\bf f(x)=\sqrt{x}~\hspace{7em}\stackrel{\textit{up by 1}}{D=1}\qquad \stackrel{\textit{left by 9}}{C=9}
\\\\[-0.35em]
~\dotfill\\\\
g(x)=\stackrel{A}{1}\sqrt{\stackrel{B}{1}x+\stackrel{C}{0}}+\stackrel{D}{0}\implies \stackrel{\textit{shifted}}{g(x)=\stackrel{A}{1}\sqrt{\stackrel{B}{1}x+\stackrel{C}{9}}+\stackrel{D}{1}}\implies \blacktriangleright g(x)=\sqrt{x+9}+1 \blacktriangleleft

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<h3><u>Question:</u></h3>

The rectangle below has an Área of x^2 + 11x + 28 square meters and a length of x+7 meters. What expression represents the width of the rectangle?

<h3><u>Answer:</u></h3>

The expression representing width of rectangle is (x + 4) meters

<h3><u>Solution:</u></h3>

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To find: width of the rectangle

<em><u>The area of rectangle is given as:</u></em>

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<em><u>Substituting the values in given formula,</u></em>

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Cancelling (x + 7) on numerator and denominator,

\text { width }=(x+4)

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