graph the exponential function $g(x)=3^{x - 1}$. to do this, plot two points on the graph of the function…

graph the exponential function $g(x)=3^{x - 1}$. 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. domain: range:

graph the exponential function $g(x)=3^{x - 1}$. 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. domain: range:

Answer

Explanation:

Step1: Find two points on the graph

Let (x = 1), then (g(1)=3^{1 - 1}=3^{0}=1). Let (x = 2), then (g(2)=3^{2 - 1}=3^{1}=3). So two points are ((1,1)) and ((2,3)).

Step2: Determine the asymptote

For an exponential function of the form (y = a^{x - h}+k), in (g(x)=3^{x - 1}), (a = 3), (h = 1), (k = 0). The horizontal - asymptote is (y = 0).

Step3: Find the domain

Since we can substitute any real number for (x) in the function (g(x)=3^{x - 1}), the domain is all real numbers. In interval notation, the domain is ((-\infty,\infty)).

Step4: Find the range

Because the exponential function (y = 3^{x - 1}) is always positive (the base (a = 3>1) and there is no vertical shift that would change the sign of the function values), the range is ((0,\infty)).

Answer:

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