Graph the logarithmic function \( g(x)=-\log _{2} x+1 \). To do this, plot two points on the graph of the function, and also draw the asymptote. Then, click on the graph-a-function button. Additionally, give the domain and range of the function using interval notation.

To plot the logarithmic function \( g(x) = -\log_2 x + 1 \), let's start by determining two key points. 1. **Choosing values of \( x \)**: - For \( x = 1 \): \[ g(1) = -\log_2(1) + 1 = -0 + 1 = 1 \] So the point is \( (1, 1) \). - For \( x = 2 \): \[ g(2) = -\log_2(2) + 1 = -1 + 1 = 0 \] So the point is \( (2, 0) \). 2. **Asymptote**: Since the logarithmic function approaches negative infinity as \( x \) approaches 0 from the right, the vertical line \( x = 0 \) is a vertical asymptote. Now, regarding the domain and range: - **Domain**: The logarithmic function is defined for \( x > 0 \), so the domain in interval notation is \( (0, \infty) \). - **Range**: Since the function goes to infinity as \( x \) increases (i.e., when \( x \) is larger), and approaches 1 as \( x \) approaches 0 from the right, the range in interval notation is \( (-\infty, 1) \). Now you can go ahead and graph the function, plot the points \( (1, 1) \) and \( (2, 0) \), and remember to draw the vertical asymptote at \( x = 0 \). Happy graphing!