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The logarithmic functions, f(x) and g(x), are shown on the graph.

What is the equation that represents g(x)? Explain your reasoning.

The Logarithmic Functions Fx And Gx Are Shown On The Graph What Is The Equation That Represents Gx Explain Your Reasoning class=

Sagot :

semsee45

Answer:

[tex]g(x)=\log (x+1)+4[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Parent function:  [tex]f(x)=\log x[/tex]

From inspection of the graph, the parent function has been translated 1 unit left and 4 units up.

Function translated 1 unit left:  [tex]f(x+1)=\log (x+1)[/tex]

Function translated 4 units up:  [tex]f(x+1)+4=\log (x+1)+4[/tex]

Therefore:

[tex]g(x)=\log (x+1)+4[/tex]

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