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Exponential GraphCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! The exponential graph function with base b is defined byf(x) = b^{x} ; where b > 0 , b≠ 1, and x is any real number. Characteristics of ExponentialGraph: 1) graph crosses the yaxis at (0,1) 2) when b > 1, the graph increases 3) when 0 < b < 1, the graph decreases 4) the domain is all real numbers 5) the range is all positive real numbers (never zero) 6) graph passes the vertical line test > it is a function 7) graph passes the horizontal line test > its inverse is also a function. 8) graph is asymptotic to the xaxis > gets very, very close to the xaxis but does not touch it or cross it. Example : 1) y = b ^{x} , b>1 , the graph will be increasing from right to left in upward direction i.e. from negative xaxis to positive yaxis. Example : 2) y =  b ^{x} , b<1, the graph will be decreasing right to left in downward direction i.e. from negative xaxis to negative yaxis. Example : 3) y = b ^{x} when the exponent is negative. The graph will be from left to right in upward direction i.e. from positive xaxis to positive yaxis. Example : 4) y = b ^{x} + c , first draw a graph of y = b ^{x} as there is + c the graph will be shifted to ‘c’ units up from the graph of y = b ^{x} Example : 5) y = b ^{x}  c , the graph shifted ‘c’ units down from the graph of y = b ^{x} Example : Natural exponentialgraph The function is defined by f(x) = e ^{x} is called the Natural Exponential Function. ( e is an irrational number ) The inverse of the exponential function is the Logarithmic function. Exponential graph Graph Dictionary Home Page Covid19 has affected physical interactions between people. Don't let it affect your learning.
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