graph the exponential function $g(x)=4^{x}+2$. to do this, plot two points on the graph of the function, and…

graph the exponential function $g(x)=4^{x}+2$. 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.

graph the exponential function $g(x)=4^{x}+2$. 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.

Answer

Explanation:

Step1: Find two points

When (x = 0), (g(0)=4^{0}+2=1 + 2=3). So one point is ((0,3)). When (x = 1), (g(1)=4^{1}+2=4 + 2=6). So another point is ((1,6)).

Step2: Determine the asymptote

For the exponential - function of the form (y = a^{x}+k) ((a>0,a\neq1)), the horizontal asymptote is (y = k). For (g(x)=4^{x}+2), the horizontal asymptote is (y = 2).

Step3: Find the domain

The domain of an exponential function (y = a^{x}+k) is all real numbers. In interval notation, the domain is ((-\infty,\infty)).

Step4: Find the range

Since (4^{x}>0) for all real (x), then (4^{x}+2>2). In interval notation, the range is ((2,\infty)).

Answer:

Two points: ((0,3)) and ((1,6)); Asymptote: (y = 2); Domain: ((-\infty,\infty)); Range: ((2,\infty))