graph the exponential function. g(x) = 4/3 e^(x - 3)+2 plot two points on the graph of the function, and…

Explanation:

Step1: Find the horizontal - asymptote

For an exponential function of the form $y = a\cdot e^{x - h}+k$, the horizontal asymptote is $y = k$. In the function $g(x)=\frac{4}{3}e^{x - 3}+2$, $k = 2$, so the horizontal asymptote is $y = 2$.

Step2: Find the first point

Let $x = 3$. Then $g(3)=\frac{4}{3}e^{3 - 3}+2=\frac{4}{3}\times e^{0}+2=\frac{4}{3}\times1 + 2=\frac{4 + 6}{3}=\frac{10}{3}\approx3.33$. So the point is $(3,\frac{10}{3})$.

Step3: Find the second point

Let $x = 4$. Then $g(4)=\frac{4}{3}e^{4 - 3}+2=\frac{4}{3}e+2\approx\frac{4}{3}\times2.718+2=\frac{10.872}{3}+2 = 3.624+2=5.624$. So the point is $(4,5.624)$.

Answer:

Horizontal asymptote: $y = 2$. Points: $(3,\frac{10}{3})$ and $(4,5.624)$