Questions: Find a. Graph the exponential function. f(x)=2^x Plot five points on the graph of the function, and also draw the asymptote.

Transcript text: Find a. Graph the exponential function. \[ f(x)=2^{x} \] Plot five points on the graph of the function, and also draw the asymptote.

Solution

Solution Steps

Step 1: Identify the function to be graphed

The function to be graphed is $ f(x) = 2^x $.

Step 2: Plot five points on the graph

To plot five points, we can choose $ x = -2, -1, 0, 1, 2 $:

$ f(-2) = 2^{-2} = 0.2500 $
$ f(-1) = 2^{-1} = 0.5000 $
$ f(0) = 2^{0} = 1.0000 $
$ f(1) = 2^{1} = 2.0000 $
$ f(2) = 2^{2} = 4.0000 $

Step 3: Identify the asymptote

The asymptote for the function $ f(x) = 2^x $ is the x-axis, or $ y = 0 $.

Final Answer

The function to be graphed is $ f(x) = 2^x $, with the asymptote $ y = 0 $.

{"axisType": 3, "coordSystem": {"xmin": -3, "xmax": 3, "ymin": -1, "ymax": 5}, "commands": ["y = 2**x", "y = 0"], "latex_expressions": ["$f(x) = 2^x$", "$y = 0$"]}

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