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The function f(x)=4∙2^x is graphed to the right. Sketch a graph of the function g(x) represented by the rule g(x)=f(x-2)+3. Mark the asymptote to help make your graph clear.

The function fx42x is graphed to the right Sketch a graph of the function gx represented by the rule gxfx23 Mark the asymptote to help make your graph clear class=
The function fx42x is graphed to the right Sketch a graph of the function gx represented by the rule gxfx23 Mark the asymptote to help make your graph clear class=

Respuesta :

Given:

[tex]f(x)=4\cdot2^x[/tex]

The rule for function g(x) is,

[tex]g(x)=f(x-2)+3[/tex]

The function becomes,

[tex]\begin{gathered} f(x)=4\cdot2^x \\ f(x-2)=4\cdot2^{x-2}=4\cdot\frac{2^x}{2^2}=2^x \\ f(x-2)+3=2^x+3 \end{gathered}[/tex]

Therefore,

[tex]g(x)=f(x-2)+3=2^x+3[/tex]

The graph of the function g(x) is,

Ver imagen ClarityS348758

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