f(x)=2^x\nplot five points on the graph of the function, and also draw the asymptote. then click on the…
f(x)=2^x\nplot five points on the graph of the function, and also draw the asymptote. then click on the graph - a - function button.
Answer
Explanation:
Step1: Choose x - values
Let (x=- 2,-1,0,1,2).
Step2: Calculate y - values for (x = - 2)
Substitute (x=-2) into (y = 2^{x}), we get (y=2^{-2}=\frac{1}{4}=0.25). The point is ((-2,0.25)).
Step3: Calculate y - values for (x=-1)
Substitute (x = - 1) into (y = 2^{x}), we get (y=2^{-1}=\frac{1}{2}=0.5). The point is ((-1,0.5)).
Step4: Calculate y - values for (x = 0)
Substitute (x = 0) into (y = 2^{x}), we get (y=2^{0}=1). The point is ((0,1)).
Step5: Calculate y - values for (x = 1)
Substitute (x = 1) into (y = 2^{x}), we get (y=2^{1}=2). The point is ((1,2)).
Step6: Calculate y - values for (x = 2)
Substitute (x = 2) into (y = 2^{x}), we get (y=2^{2}=4). The point is ((2,4)).
Step7: Determine the asymptote
For the exponential function (y = 2^{x}), the horizontal asymptote is (y = 0) (as (x\to-\infty), (y\to0)).
Answer:
The five points are ((-2,0.25),(-1,0.5),(0,1),(1,2),(2,4)) and the horizontal asymptote is (y = 0).