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

Explanation:

Step1: Find the horizontal asymptote

For an exponential function of the form $y = a\cdot e^{x - h}+k$, the horizontal asymptote is $y = k$. Here $a=\frac{1}{3}$, $h = 1$ and $k = 3$, so the horizontal asymptote is $y=3$.

Step2: Find the first - point

Let $x = 1$. Then $g(1)=\frac{1}{3}e^{1 - 1}+3=\frac{1}{3}\times e^{0}+3=\frac{1}{3}\times1 + 3=\frac{1 + 9}{3}=\frac{10}{3}$. So the point is $(1,\frac{10}{3})$.

Step3: Find the second - point

Let $x = 2$. Then $g(2)=\frac{1}{3}e^{2 - 1}+3=\frac{1}{3}e+3\approx\frac{1}{3}\times2.718+3 = 0.906+3=3.906$. So the point is $(2,3.906)$.

Answer:

Horizontal asymptote: $y = 3$. Points: $(1,\frac{10}{3})$ and $(2,3.906)$