graph the exponential function.\ng(x)=2e^{x + 4}-4\nplot two points on the graph of the function, and also…

graph the exponential function.\ng(x)=2e^{x + 4}-4\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.\ng(x)=2e^{x + 4}-4\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

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

Step2: Find the first point

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

Step3: Find the second point

Let $x=-3$. Then $g(-3)=2e^{-3 + 4}-4=2e^{1}-4\approx2\times2.718 - 4=5.436 - 4 = 1.436$. So the point is $(-3,1.436)$.

Answer:

Horizontal asymptote: $y = - 4$. Points: $(-4,-2)$ and $(-3,1.436)$