Need help!!!!!!!!!!!!!!!!

Mathematics

1 answer:

storchak [24]3 years ago

5 0

Answer:

g(x) = $-\frac{2}{5} (10)^{x}$

Step-by-step explanation:

Looking at the equation of a Exponential Function:

The a-value $(\frac{2}{5})$ determines whether the function reflects over the x-axis. If it's negative it reflects over the x-axis. If it's positive it stays over the x-axis.

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3 years ago

How to solve this question

Fiesta28 [93]

7 = 5y - 3
add 3 to both sides
10 = 5y
divide both sides by 5
2 = y
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2 = 5y
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2/5 = y
-3 = 5y - 3
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0 = 5y
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6 = 5y - 3
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9 = 5y
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9/5 = y
-8 = 5y - 3
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3 years ago

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

ch4aika [34]

$\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
f(x)= A( Bx+ C)+ D
\\\\
~~~~y= A( Bx+ C)+ D
\\\\
f(x)= A\sqrt{ Bx+ C}+ D
\\\\
f(x)= A(\mathbb{R})^{ Bx+ C}+ D
\\\\
f(x)= A sin\left( B x+ C \right)+ D
\\\\[-0.35em]
~\dotfill\\\\
\bullet \textit{ stretches or shrinks horizontally by } A\cdot B\\\\
\bullet \textit{ flips it upside-down if } A\textit{ is negative}\\
~~~~~~\textit{reflection over the x-axis}
\\\\
\bullet \textit{ flips it sideways if } B\textit{ is negative}$

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

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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