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timofeeve [1]
3 years ago
14

Suppose f(x) = x³ . find the graph of f(x+5)

Mathematics
2 answers:
Ganezh [65]3 years ago
5 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}

and with that template in mind,

notice from a parent function of   f(x) = x³,
a derived function with f(x+5) = (x + 5)³

has a C component of 5, C = 5, which means is the as the parent, just shifted to the left by 5 units.
Sedaia [141]3 years ago
5 0
To move a function to the left by c units, add c to every xso f(x) shifted to the left by 5 units is f(x+5)
for f(x)=x^3, the shifted graph would be f(x+5)=(x+5)^3 it would be the same graph except that it's shifted to the left 5 units ( passes through (-5,0) instead of (0,0) )

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