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larisa86 [58]
3 years ago
7

The function f(x)=2^x and g(x)=f(x+k). If k=-5,what can be concluded about the graph of g(x)?

Mathematics
2 answers:
melamori03 [73]3 years ago
8 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}\\
~~~~~~\textit{reflection over the y-axis}
\\\\
\bullet \textit{ horizontal shift by }\frac{  C}{  B}\\
~~~~~~if\ \frac{  C}{  B}\textit{ is negative, to the right}

\bf ~~~~~~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

\bf f(x)=2^x\qquad 
\begin{cases}
g(x)=f(x+k)&k=5\\
\qquad\quad f(x+5)\\
\qquad \quad 2^{x+5}
\end{cases}

notice, in g(x)

B = 1, no change from parent

C= +2



Artist 52 [7]3 years ago
3 0

Answer:    

The graph of g(x) is obtained by translating the function of f(x) by shifting the graph to right by 5 units

Step-by-step explanation:

The function f(x) is given to be :

f(x)=2^x

Also, The function g(x) is given to be : g(x) = f(x + k)

Now, The value of k = -5

So, The function g(x) becomes g(x) = f(x - 5)

The function f(x - 5) shows that the function is translated by shifting the graph of f(x) to right by 5 units.

Thus, The graph of g(x) is obtained by translating the function of f(x) by shifting the graph to right by 5 units

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