Respuesta :
[tex]\bf ~~~~~~~~~~~~\textit{function transformations}
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% templates
f(x)= A( Bx+ C)+ D
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~~~~y= A( Bx+ C)+ D
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f(x)= A\sqrt{ Bx+ C}+ D
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f(x)= A(\mathbb{R})^{ Bx+ C}+ D
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f(x)= A sin\left( B x+ C \right)+ D
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--------------------[/tex]
[tex]\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}[/tex]
[tex]\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}[/tex]
with that template in mind
[tex]\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}[/tex]
notice, in g(x)
B = 1, no change from parent
C= +2
[tex]\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}[/tex]
[tex]\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}[/tex]
with that template in mind
[tex]\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}[/tex]
notice, in g(x)
B = 1, no change from parent
C= +2
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 :
[tex]f(x)=2^x[/tex]
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
