graph the logarithmic function $g(x)=-2 - \\log_3x$. to do this, plot two points on the graph of the…

graph the logarithmic function $g(x)=-2 - \\log_3x$. 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.

graph the logarithmic function $g(x)=-2 - \\log_3x$. 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.

Answer

Explanation:

Step1: Find the vertical - asymptote

The argument of the logarithm must be positive. For $y = - 2-\log_{3}x$, the vertical asymptote occurs when $x = 0$.

Step2: Find two points on the graph

When $x = 1$: $g(1)=-2-\log_{3}1=-2 - 0=-2$. So the point is $(1, - 2)$. When $x = 3$: $g(3)=-2-\log_{3}3=-2 - 1=-3$. So the point is $(3,-3)$.

Step3: Determine the domain

The argument of the logarithmic function $y=\log_{3}x$ is $x>0$. So the domain of $g(x)=-2 - \log_{3}x$ is $(0,\infty)$.

Step4: Determine the range

Since the range of the basic logarithmic function $y = \log_{3}x$ is $(-\infty,\infty)$, the range of $g(x)=-2-\log_{3}x$ is also $(-\infty,\infty)$.

Answer:

Domain: $(0,\infty)$ Range: $(-\infty,\infty)$