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

graph the exponential function. g(x)=2e^x - 4 - 2 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)=2e^x - 4 - 2 plot 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

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

Step2: Find the first point

Let $x = 4$. Then $g(4)=2e^{4 - 4}-2=2e^{0}-2=2\times1 - 2=0$. So the point is $(4,0)$.

Step3: Find the second point

Let $x = 5$. Then $g(5)=2e^{5 - 4}-2=2e^{1}-2=2e - 2\approx2\times2.718 - 2=5.436 - 2 = 3.436$. So the point is $(5,2e - 2)\approx(5,3.44)$.

Answer:

Horizontal asymptote: $y=-2$, Points: $(4,0)$ and $(5,2e - 2)\approx(5,3.44)$