graph the exponential function.\n\n$g(x)=\frac{1}{2}e^{x - 1}-1$\n\nplot two points on the graph of the…

graph the exponential function.\n\n$g(x)=\frac{1}{2}e^{x - 1}-1$\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$g(x)=\frac{1}{2}e^{x - 1}-1$\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 horizontal - asymptote

As $x\to-\infty$, $e^{x - 1}\to0$. So, $y = - 1$ is the horizontal asymptote.

Step2: Find the first point

Let $x = 1$. Then $g(1)=\frac{1}{2}e^{1 - 1}-1=\frac{1}{2}\times1 - 1=-\frac{1}{2}$. So the point is $(1,-\frac{1}{2})$.

Step3: Find the second point

Let $x = 2$. Then $g(2)=\frac{1}{2}e^{2 - 1}-1=\frac{1}{2}e-1\approx\frac{1}{2}\times2.718 - 1=0.359$. So the point is $(2,0.359)$.

Answer:

Horizontal asymptote: $y=-1$. Points: $(1,-\frac{1}{2})$ and $(2,0.359)$