Exponential Graphs

 

EXPONENTIAL GRAPHS                                 


 Exponential means a very rapid increase. An exponential graph shows this through a very steep curve. An exponential graph is formed from the equation of :

f(x)=a^x

This equation is never crosses the x axis, this is because a to the power of anything would never equal to 0 or become negative, the graph goes on till 'infinty', unless numbers are be added and/or multiplied to change the curve.

These are some exponential graphs:


It might be unclear from the naked eye but the graphs don't intercept/touch the x-axis but keep going closer towards it! 

As you can see, the greater the number, the steeper the graph.

All graphs cross the point (1,0) as anything to the power of 0 ( the x value) will be 1( the y value)!

But what happens if we multiply the 'x' and not the number in the equation?



The graph of 2^2x is steeper! 



If we add/ subtract a number the graph will just shift up/down by that number!



But what happens if we add a number to the 'x' value?


Here the two curves remain parallel to each other but the 2^(x+3) curve has 'stretched' vertically. This is because now for every 'x' value, instead of 2^x, it is 2^(x+3)!



Question:



Draw the graph of y=4^x and 4^x +1






Solution:



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