Question

WHEN LOGARITHMIC FUNCTIONS ARE GRAPHED WHICH TRANSFORMATION WILL RESULT IN A Y INTERCEPT?

Answer 1

Horizontal translation left c units, f(x) = log(x + c)

Explanation:

The logarithmic function, f(x) = log(x), doesn't has a y-intercept. The only transformation that will result in a y-intercept is horizontal translation left c units, where now f(x) = log(x + c). Other transformation of the parent function like vertical translation (up or down), horizontal translation to the right, reflections over x or y axis, vertical stretching or compression, or horizontal stretching or compression, doesn't result in a y-intercept.

Answer 2

The graph of the function LOG has no y-intercept, but has an x-intercept.
However, if we apply a symmetry toward the line y=x, then the graph
will result in an y-intercept.
Check that by drawing