graph the exponential function g(x)=3^(x + 1). to do this, plot two points on the graph of the function, and…

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.

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.

Answer

Explanation:

Step1: Find two points on the function

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

Step2: Determine the asymptote

For an exponential - function of the form (y = a\cdot b^{x + h}+k), in the function (g(x)=3^{x + 1}), which can be written as (y = 3\cdot3^{x}), the horizontal asymptote is (y = 0) since there is no vertical shift ((k = 0)).

Step3: Find the domain

The domain of an exponential function (y = b^{x}) (in this case (y = 3^{x+1})) is all real numbers. In interval notation, the domain is ((-\infty,\infty)).

Step4: Find the range

Since the horizontal asymptote is (y = 0) and the function (y = 3^{x+1}) is always positive (because (b = 3>0)), the range is ((0,\infty)).

Answer:

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