Question

Compare the graphs below of the logarithmic functions. Write the equation to represent g(x). g(x) = log(x) − 4 g(x) = log(x) + 4 g(x) = log(x + 4) g(x) = log(x − 4) (Picture Below)

Answer 1

The equation that represents the graph of g(x) is g(x) = log(x - 4)

The equation of f(x) is represented as:

$f(x) = log(x)$

From the graph, the function f(x) is shifted to the right by 4 units.

The rule of this transformation is:

$(x,y) \to (x -4,y)$

So, we have:

$g(x) = f(x-4)$

Given that:

$f(x) = log(x)$

The equation becomes

$f(x - 4) = log(x -4)$

So, we have:

$g(x) = log(x -4)$

Hence, the equation that represents the graph of g(x) is g(x) = log(x - 4)

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