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

graph the exponential function. g(x)=1/2*e^(x + 4)-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)=1/2*e^(x + 4)-4 plot two points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.

Answer

Answer:

To find two - points:

  1. When (x=-4):
    • Substitute (x = - 4) into (g(x)=\frac{1}{2}e^{x + 4}-4).
    • (g(-4)=\frac{1}{2}e^{-4 + 4}-4=\frac{1}{2}e^{0}-4=\frac{1}{2}\times1 - 4=\frac{1}{2}-4=-\frac{7}{2}=-3.5). So the point is ((-4,-3.5)).
  2. When (x=-3):
    • Substitute (x=-3) into (g(x)=\frac{1}{2}e^{x + 4}-4).
    • (g(-3)=\frac{1}{2}e^{-3 + 4}-4=\frac{1}{2}e^{1}-4=\frac{e}{2}-4\approx\frac{2.718}{2}-4 = 1.359-4=-2.641). So the point is ((-3,-2.641)). The horizontal asymptote: For an exponential function of the form (y = ae^{bx}+c), the horizontal asymptote is (y = c). In the function (g(x)=\frac{1}{2}e^{x + 4}-4), (c=-4), so the horizontal asymptote is (y = - 4).

Explanation:

Step1: Find first point

Substitute (x=-4) into (g(x)) (g(-4)=\frac{1}{2}e^{-4 + 4}-4=\frac{1}{2}-4=-\frac{7}{2})

Step2: Find second point

Substitute (x = - 3) into (g(x)) (g(-3)=\frac{1}{2}e^{-3 + 4}-4=\frac{e}{2}-4)

Step3: Determine asymptote

Use form (y = ae^{bx}+c) Asymptote is (y=-4)