graph the exponential function. g(x)=1/2e^(x - 1)+4 plot two points on the graph of the function, and also…

graph the exponential function. g(x)=1/2e^(x - 1)+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)=1/2e^(x - 1)+4 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 asymptote

The general form of an exponential - function is $y = a\cdot e^{x - h}+k$. For the function $g(x)=\frac{1}{2}e^{x - 1}+4$, the horizontal asymptote is $y = 4$ because as $x\to-\infty$, $e^{x - 1}\to0$, and $y\to4$.

Step2: Find the first point

Let $x = 1$. Then $g(1)=\frac{1}{2}e^{1 - 1}+4=\frac{1}{2}\times e^{0}+4=\frac{1}{2}\times1 + 4=\frac{1 + 8}{2}=4.5$. So the point is $(1,4.5)$.

Step3: Find the second point

Let $x = 2$. Then $g(2)=\frac{1}{2}e^{2 - 1}+4=\frac{1}{2}e+4\approx\frac{1}{2}\times2.718+4 = 1.359+4=5.359$. So the point is $(2,5.359)$.

Answer:

Asymptote: $y = 4$; Points: $(1,4.5)$ and $(2,5.359)$