Mathematics, 09.07.2019 23:30 strad08
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 units .
Answers: 1
![\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}](/tpl/images/0071/1747/a6c7e.png)
![\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](/tpl/images/0071/1747/7f3ef.png)
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Write a formula for the function g(x) obtained when the graph of f(x)= square root x is shifted up 1...
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