a. graph the function f(x)=e^x on the window -5,5 by -10,30. b. find f(1), f(-5), and f(4), rounded to three…

Explanation:

Step1: Graph the function

Use a graph - ing utility (like a graphing calculator or software such as Desmos). Enter the function (y = e^{x}) and set the (x) - window to ([-5,5]) and the (y) - window to ([-10,30]).

Step2: Calculate function values

For (f(1)): Substitute (x = 1) into (f(x)=e^{x}), so (f(1)=e^{1}\approx2.718). For (f(-5)): Substitute (x=-5) into (f(x)=e^{x}), so (f(-5)=e^{-5}=\frac{1}{e^{5}}\approx\frac{1}{148.413}\approx0.007). For (f(4)): Substitute (x = 4) into (f(x)=e^{x}), so (f(4)=e^{4}\approx54.598).

Step3: Find horizontal asymptote

As (x\to-\infty), (y = e^{x}\to0). So the horizontal asymptote is (y = 0).

Step4: Find y - intercept

Set (x = 0) in (f(x)=e^{x}). Then (f(0)=e^{0}=1).

Answer:

a. Use a graph - ing utility to graph. b. (f(1)\approx2.718), (f(-5)\approx0.007), (f(4)\approx54.598) c. (y = 0) d. (y = 1)