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Sindrei [870]
3 years ago
14

What change do you have to make to the graph of f (x) = 7x in order to graph the function g (x) = 7x+10?

Mathematics
1 answer:
cricket20 [7]3 years ago
4 0
\bf ~~~~~~~~~~~~\textit{function transformations}
\\\\\\
% templates
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
\\\\
--------------------

\bf \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}

now, with that template in mind, let's see

 \bf \stackrel{parent}{f(x)=7x}\qquad \qquad \qquad \stackrel{transformed}{g(x)=7x\stackrel{D}{+10}}

D = 10, upwards shift of 10 units.
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