If a<\/em><\/strong> is greater than 1, the function continuously increases in value with the increase of x<\/em><\/strong>. A special property of exponential functions is that the slope<\/strong> of the function also continuously increases as x<\/em> increases. Instead of writing ax<\/sup><\/em><\/strong> we can write the same thing as a^x<\/em><\/strong> where the symbol ^<\/em><\/strong> is a sign for power<\/em><\/strong>. Even in the computer programs and in the calculators this sign is used to represent the powers.<\/p>\n Here, if we restrict the values of a<\/em><\/strong> to the positive numbers then the domain will be the set of all real numbers.<\/p>\n The following graph represents the exponential functions f(x) and g(x) where a>1 for f(x) and 0<a<1 for g(x).<\/p>\n Exponential function is a function which is of the form f(x)=ax<\/sup> + b<\/em><\/strong>, where x<\/em><\/strong> is the exponent or power of a<\/em><\/strong>, where a<\/em><\/strong> is any constant and b<\/em><\/strong> is any expression. Unless, an exponential function is transformed, it always passes through (0,1) (because a0<\/sup> =1<\/em><\/strong>) and does not cross the x-axis (because ax<\/sup>\u22600<\/em><\/strong> for any value of x<\/em><\/strong>) .<\/p>\n Example:<\/strong><\/p>\n Graph of 2x<\/sup>.<\/p>\n Solution:<\/strong><\/p>\n Let us find a table of values by substituting different values for x<\/em><\/strong>.<\/p>\n![\"\"](\"https:\/\/SchoolTutoring.com\/wp-content\/uploads\/sites\/2\/2012\/10\/exponential1.jpg\" "\\"exponential1\\"")
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