Sketch the exponental graph of f( x )=2x and g( x )= 1/2 , Mathematics

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Example Sketch the graph of following

f( x ) = 2x  and  g( x ) = ( 1 /2)x

Solution

Let's firstly make a table of values for these two functions.

545_exponental function.png

Following is the sketch of both of these functions.

2399_exponental graph.png

This graph shows some very nice properties regarding exponential functions in general.

Properties of f( x ) = b x

1.   f(0)= 1.  The function will take the value of 1 at x=0 always

2.   f( x ) ≠ 0 .  An exponential function will never get zero.

3.   f( x ) > 0 .  An exponential function is always get positive.

4.   The previous two properties can be summarized through saying that the range of an exponential function is (0, ∞ ) .

5.   The domain of exponential function is [ -∞, ∞ ] . In other terms, you can plug every x in an exponential function.

6.   If 0 < b < 1 then,

a.   f ( x ) → 0   as x → ∞

b.   f ( x ) → ∞ as  x → -∞

7.  If b >1 then,

a.  f (x ) → ∞ as   x → ∞

b.  f ( x ) → 0   as x → -∞

These will all be extremely useful properties to remember .


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