document.write( "Question 1206248: what would the graph of an exponential function with range y<1,y∈R and a y-intercept of 0 look like. And what are the domain, horizontal asymptote, x-intercept. \n" ); document.write( "

Algebra.Com's Answer #843549 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "        The goal of this my post is twofold.\r
\n" ); document.write( "\n" ); document.write( "        First is to make a correction in Edwin's post.\r
\n" ); document.write( "\n" ); document.write( "        Second is to expand it and to show another examples of similar functions.\r
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document.write( "In his post, Edwin, actually, found a function  y = , satisfying the imposed conditions\r\n" );
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document.write( "But he mistakenly wrote it as  y = .\r\n" );
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document.write( "Here \"2\" is a mistake or a typo. The correct formula for the function is  y = .\r\n" );
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document.write( "    Its domain is  .\r\n" );
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document.write( "    Its horizontal asymptote is  .\r\n" );
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document.write( "    Its x-intercept (and its y-intercept) is (0,0). \r\n" );
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document.write( "Actually, there are infinitely many of such functions, satisfying the imposed conditions.\r\n" );
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document.write( "They are of the form  y = , with positive real coefficient \"a\" in the exponent.\r\n" );
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document.write( "In this plot, red curve is for a = 1; green curve is for a = 2 and blue curve is for a = 0.5.\r\n" );
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document.write( "    Their domain is  .\r\n" );
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document.write( "    Their horizontal asymptote is  .\r\n" );
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document.write( "    Their x-intercept (and their y-intercept) is (0,0). \r\n" );
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document.write( "There are solutions of another form. \r\n" );
document.write( "They are of the form  y = , with NEGATIVE real coefficient \"a\" in the exponent.\r\n" );
document.write( "They also satisfy all imposed conditions.\r\n" );
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document.write( "See the plots below\r\n" );
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document.write( "In this plot, red curve is for a = -1; green curve is for a = -2 and blue curve is for a = -0.5.\r\n" );
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document.write( "    Their domain is the same  .\r\n" );
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document.write( "    Their horizontal asymptote is  .\r\n" );
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document.write( "    Their x-intercept (and their y-intercept) is (0,0). \r\n" );
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