Question

Compare the graphs below of the logarithmic functions. Write the equation to represent g(x).

Answer 1

Answer:

g(x)=log(x-4)

Step-by-step explanation:

Since its moving left and right, the number has to be inside the parenthesis. Therefore, g(x)=log(x-4)

Answer 2

Answer:

The equation to represent g(x) will be $g(x)=log(x)+4$

Step-by-step explanation:

Considering the logarithmic function

$f(x)=log(x)$

As we know that when a constant c gets added to the parent function, the result would be a vertical shift c units in the direction of the sign of c.

So,

$g(x)=log(x)+4$ is basically the shift up by 4 units, and the graph also showing the same situation.

Therefore, the equation to represent g(x) will be $g(x)=log(x)+4$

Also, the graphs of both $f(x)=log(x)$ and  $g(x)=log(x)+4$ is attached where black mark graph represents  $f(x)=log(x)$ and red mark graph represents $g(x)=log(x)+4$.

Keywords: transformation, vertical shift, graph

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