graph the exponential function.\ng(x)=4e^{x - 4}-1\nplot two points on the graph of the function, and also…

Explanation:

Step1: Find the horizontal asymptote

As $x\to-\infty$, $e^{x - 4}\to0$. So, $y=- 1$ is the horizontal asymptote since $\lim_{x\to-\infty}(4e^{x - 4}-1)=4\times0 - 1=-1$.

Step2: Find the first - point

Let $x = 4$. Then $g(4)=4e^{4 - 4}-1=4\times e^{0}-1=4\times1 - 1=3$. So the point is $(4,3)$.

Step3: Find the second - point

Let $x = 5$. Then $g(5)=4e^{5 - 4}-1=4e^{1}-1=4e-1\approx4\times2.718 - 1=10.872-1 = 9.872$. So the point is $(5,9.872)$.

Answer:

Horizontal asymptote: $y = - 1$. Points: $(4,3)$ and $(5,9.872)$