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

graph the exponential function. g(x)=4/3 e^x + 3 - 4 plot 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. g(x)=4/3 e^x + 3 - 4 plot two points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

Answer

Answer:

To plot points:

  • When (x=-3), (g(-3)=\frac{4}{3}e^{-3 + 3}-4=\frac{4}{3}-4=-\frac{8}{3}\approx - 2.67). So one point is ((-3,-\frac{8}{3})).
  • When (x=-2), (g(-2)=\frac{4}{3}e^{-2 + 3}-4=\frac{4}{3}e-4\approx\frac{4}{3}\times2.718 - 4=3.624 - 4=-0.376). So another point is ((-2,\frac{4}{3}e - 4)). The horizontal - asymptote of the exponential function (g(x)=\frac{4}{3}e^{x + 3}-4) is (y = - 4).

Explanation:

Step1: Find the first point

Substitute (x=-3) into (g(x)=\frac{4}{3}e^{x + 3}-4).

Step2: Find the second point

Substitute (x = - 2) into (g(x)=\frac{4}{3}e^{x+3}-4).

Step3: Determine the asymptote

For an exponential function of the form (y = ae^{x - h}+k), the horizontal asymptote is (y = k). Here (k=-4).