Question

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

Answer 1

We can see that g(x) is a translation of 4 units to the left of f(x), then:

g(x) = log₃(x + 4).

How to get the equation that represents g(x)?

Here we can see that g(x) is a shift of f(x). Is clear that the asymptote of g(x) is 4 units to the left of the asymptote of f(x), so we can say that g(x) is a shift of 4 units to the left of f(x).

Remember that for a given function f(x), an horizontal shift of N units is given by:

g(x) = f(x + N).

• If N is positive, the shift is to the left.
• If N is positive, the shift is to the right.

Then a shift of 4 units to the left is written as:

g(x) = log₃(x + 4).

Then the correct option is the last one.

If you want to learn more about translations:

brainly.com/question/24850937

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