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 #843544 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "We want a graph like this. \r\n" );
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document.write( "One that goes through the origin to have a y=intercept of 0. \r\n" );
document.write( "It must go up, as close to 1 as possible, but never quite to 1,\r\n" );
document.write( "because it has a range of y < 1, so it has a horizontal asymptote at y=1\r\n" );
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document.write( "How do we get an equation for a graph to look like that?\r\n" );
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document.write( "We start with the basic exponential equation.\r\n" );
document.write( ". It has a range of x > 0, and horizontal asymptote y=0,\r\n" );
document.write( "which is the x-axis\r\n" );
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document.write( "We want to get it below the x-axis, so we reflect it in the x-axis by\r\n" );
document.write( "multiplying the right side by -1\r\n" );
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document.write( "Now all we need to do is shift the graph and its horizontal asymptote\r\n" );
document.write( "2 units upward, by adding +1 to the right side. That will take care of\r\n" );
document.write( "both raising the asymptote from y=0 to y=1 and the y-intercept of -1 up to 0.\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( "Edwin

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