Question

Determine the function which corresponds to the given graph. The asymptote is x = -3.

Answer 1

Answer:

y = log (x + 3)

Step-by-step explanation:

This function (graph) is a translated version of the log function.

The basic graph of y = log(x) is attached.

As we can compare, we see that the basic logx graph goes through (1,0) and the asymptote is x = 0

This graph, is basically translated 3 units left, so the point becomes (1-3,0) = (-2,0) and the asymptote becomes x = -3.

THis conforms with the graph shown.

Thus, we need to horizontally translate y = log x 3 units left, which means:

y = log (x + 3)

Note: if we have a horizontal translation of a units to the left, y = logx becomes y = log(x+a)