Questions: Exponential and Logarithmic Functions Graphing a logarithmic function: Basic Graph the logarithmic function. g(x)=log(1 / 2) x Plot two points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.

Exponential and Logarithmic Functions
Graphing a logarithmic function: Basic

Graph the logarithmic function.
g(x)=log(1 / 2) x

Plot two points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.

Transcript text: Exponential and Logarithmic Functions Graphing a logarithmic function: Basic Graph the logarithmic function. \[ g(x)=\log _{1 / 2} x \] Plot two points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button.

Solution

Solution Steps

Step 1: Find two points

We are asked to graph $g(x) = \log_{1/2}x$. Let us choose two $x$ values and find their corresponding $y$ or $g(x)$ values.

$x=1$: $g(1) = \log_{1/2}(1) = 0$ So, $(1,0)$ is a point on the graph.

$x=2$: $g(2) = \log_{1/2}(2) = -1$ So, $(2, -1)$ is a point on the graph.

Step 2: Find the asymptote

The function $g(x) = \log_{1/2} x$ is defined for $x > 0$. The graph will approach the $y$-axis (i.e., $x=0$) but will never touch it. Therefore, $x=0$ is a vertical asymptote.

Step 3: Plot the points and the asymptote

Plot the points (1,0) and (2, -1) on the coordinate plane. Draw the vertical asymptote at $x=0$. Draw a smooth curve passing through the plotted points that approaches but does not touch the vertical asymptote.