Question

Determine the function which corresponds to the given graph. (3 points) a natural logarithmic function crossing the x axis at negative two and y axis at one. The asymptote is x = -3

Answer 1

`y=\log_3{(x+3)}`

Explanation:

The parent log function has a vertical asymptote at x=0, so the asymptote at x=-3 indicates a left shift of 3 units.

The parent log function crosses the x-axis 1 unit to the right of the vertical asymptote, which this one does, indicating there is no vertical shift.

The parent log function has an x-value equal to its base when it has a y-value of 1. Here, the y-value of 1 corresponds to an x-value 3 units to the right of the vertical asymptote, so the base of this logarithm is 3.

The function is ...

`\boxed{y=\log_3{(x+3)}}`