Questions: Graph the logarithmic function. g(x) = 2 + log base (1 / 3) of x Plot two points on the graph of the function, and also draw the asymptote.

Solution Steps

The vertical asymptote of a logarithmic function occurs when the argument of the logarithm is zero. In this case, the argument is _x_, so the vertical asymptote is _x_ = 0. This is the y-axis.

We can find two points by choosing _x_-values and plugging them into the function.

• If _x_ = 1, then g(1) = 2 + log_1/3(1) = 2 + 0 = 2. So, the point (1, 2) is on the graph.

• If _x_ = 3, then g(3) = 2 + log_1/3(3) = 2 + (-1) = 1. So, the point (3, 1) is on the graph.

Plot the points (1, 2) and (3, 1). Draw the vertical asymptote _x_ = 0. Sketch the curve of the logarithmic function approaching the asymptote as _x_ approaches 0 from the right, and passing through the two plotted points.

Final Answer: