graph the logarithmic function $g(x)=-log_4 x$. to do this, plot two points on the graph of the function…

graph the logarithmic function $g(x)=-log_4 x$. 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.

graph the logarithmic function $g(x)=-log_4 x$. 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.

Answer

Explanation:

Step1: Find two points

When $x = 1$, $g(1)=-\log_4 1=0$. When $x = 4$, $g(4)=-\log_4 4=- 1$. So two points are $(1,0)$ and $(4, - 1)$.

Step2: Determine the asymptote

The vertical - asymptote of the logarithmic function $y = \log_a x$ is $x = 0$. For $g(x)=-\log_4 x$, the vertical asymptote is $x = 0$.

Step3: Find the domain

The argument of the logarithm must be positive. For $y =-\log_4 x$, $x>0$. In interval notation, the domain is $(0,\infty)$.

Step4: Find the range

The range of any non - vertical shifted logarithmic function is all real numbers. So the range of $g(x)=-\log_4 x$ is $(-\infty,\infty)$.

Answer:

Two points: $(1,0)$ and $(4, - 1)$; Asymptote: $x = 0$; Domain: $(0,\infty)$; Range: $(-\infty,\infty)$