graph the exponential function.\n\n$g(x)=\\frac{1}{3}e^{x + 4}+1$\n\nplot two points on the graph of the…

graph the exponential function.\n\n$g(x)=\\frac{1}{3}e^{x + 4}+1$\n\nplot two points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

graph the exponential function.\n\n$g(x)=\\frac{1}{3}e^{x + 4}+1$\n\nplot two points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

Answer

Explanation:

Step1: Find the asymptote

For the exponential function (y = \frac{1}{3}e^{x + 4}+1), the general form of an exponential function is (y = ae^{x - h}+k). The horizontal asymptote is (y = k). Here (k = 1), so the horizontal asymptote is (y = 1).

Step2: Find two points

  • Let (x=-4): [ \begin{align*} g(-4)&=\frac{1}{3}e^{-4 + 4}+1\ &=\frac{1}{3}e^{0}+1\ &=\frac{1}{3}\times1 + 1\ &=\frac{1 + 3}{3}=\frac{4}{3}\approx1.33 \end{align*} ] So the point is ((-4,\frac{4}{3}))

  • Let (x=-3): [ \begin{align*} g(-3)&=\frac{1}{3}e^{-3 + 4}+1\ &=\frac{1}{3}e^{1}+1\ &\approx\frac{1}{3}\times2.72+1\ &=0.91+1=1.91 \end{align*} ] So the point is ((-3,\frac{e + 3}{3})\approx(-3,1.91))

Answer:

Two points ((-4,\frac{4}{3})) and ((-3,\frac{e + 3}{3})\approx(-3,1.91)) and the horizontal asymptote (y = 1) can be used to graph the function (g(x)=\frac{1}{3}e^{x + 4}+1).