graph the logarithmic function (g(x)=-log_{2}x + 2). to do this, plot two points on the graph of the…

graph the logarithmic function (g(x)=-log_{2}x + 2). 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_{2}x + 2). 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

Let (x = 1), then (g(1)=-\log_2(1)+2). Since (\log_2(1) = 0), (g(1)=2). So one point is ((1,2)). Let (x = 2), then (g(2)=-\log_2(2)+2). Since (\log_2(2)=1), (g(2)=- 1 + 2=1). So another point is ((2,1)).

Step2: Determine the asymptote

For the logarithmic function (y =-\log_2x+2), the vertical - asymptote of the basic logarithmic function (y = \log_2x) is (x = 0), and the transformation does not change the position of the vertical asymptote. So the vertical asymptote is (x = 0).

Step3: Find the domain

The argument of the logarithmic function must be positive. For (y=-\log_2x + 2), (x>0). In interval notation, the domain is ((0,\infty)).

Step4: Find the range

The range of a general logarithmic function (y = a\log_bx + c) is all real numbers. So the range of (y=-\log_2x + 2) is ((-\infty,\infty)).

Answer:

Points: ((1,2)) and ((2,1)); Asymptote: (x = 0); Domain: ((0,\infty)); Range: ((-\infty,\infty))