graph the function: $y = 2^{x}$
graph the function: $y = 2^{x}$
Answer
Explanation:
Step1: Find points on the function
When (x = - 2), (y=2^{-2}=\frac{1}{4}=0.25); when (x=-1), (y = 2^{-1}=\frac{1}{2}=0.5); when (x = 0), (y=2^{0}=1); when (x = 1), (y=2^{1}=2); when (x = 2), (y=2^{2}=4); when (x = 3), (y=2^{3}=8).
Step2: Plot the points
Plot the points ((-2,0.25)), ((-1,0.5)), ((0,1)), ((1,2)), ((2,4)), ((3,8)) on the given coordinate - grid.
Step3: Draw the curve
Connect the plotted points with a smooth curve. The curve approaches the (x) - axis as (x\to-\infty) and increases rapidly as (x\to+\infty).
Answer:
A smooth - increasing curve passing through the points ((-2,0.25)), ((-1,0.5)), ((0,1)), ((1,2)), ((2,4)), ((3,8)) and approaching the (x) - axis for negative large values of (x).