graph the logarithmic function (g(x)=-log_{3}x). to do this, plot two points on the graph of the function…

graph the logarithmic function (g(x)=-log_{3}x). 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. domain: range:

graph the logarithmic function (g(x)=-log_{3}x). 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. domain: range:

Answer

Explanation:

Step1: Find two points

When $x = 1$, $g(1)=-\log_3(1)=0$. When $x = 3$, $g(3)=-\log_3(3)= - 1$.

Step2: Determine the asymptote

The vertical - asymptote of the logarithmic function $y =-\log_3(x)$ is $x = 0$ since the argument of the logarithm $x>0$.

Step3: Find the domain

The domain of the function $y =-\log_3(x)$ is the set of all positive real numbers. In interval notation, the domain is $(0,\infty)$.

Step4: Find the range

The range of a logarithmic function of the form $y = a\log_b(x)+k$ (here $a=-1$, $b = 3$, $k = 0$) is all real numbers. In interval notation, the range is $(-\infty,\infty)$.

Answer:

Two points: $(1,0)$ and $(3, - 1)$; Asymptote: $x = 0$; Domain: $(0,\infty)$; Range: $(-\infty,\infty)$