document.write( "Question 1145473: Find the domain and range of the function f(x)=-e^-x+8 \n" ); document.write( "

Algebra.Com's Answer #766710 by Theo(13342) $\"\"$ $\"About$

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let f(x) = y
\n" ); document.write( "you get y = -e^-x + 8
\n" ); document.write( "this is equivalent to:
\n" ); document.write( "y = -1/e^x + 8
\n" ); document.write( "as x gets larger, -1/e^x becomes smaller and approaches 0.
\n" ); document.write( "that makes y approach 8.
\n" ); document.write( "as x gets smaller, e^x gets smaller which makes -1/e^x become larger until it approaches minus infinity.
\n" ); document.write( "there is no restriction to the value that x can take, therefore the domain is -infinity < x < infinity.
\n" ); document.write( "the range becomes -infinity < y < 8.
\n" ); document.write( "that's what i think.
\n" ); document.write( "the graph looks like this.\r
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\n" ); document.write( "\n" ); document.write( "you can test additional values by simply replacing x with random numbers such as 10, 50, 100, 0, -10, -50, -100
\n" ); document.write( "you'll get values up to the ability of the calculator to handle the largeness or the smallness of the value of y.
\n" ); document.write( "for example:
\n" ); document.write( "y = -1/e^50 + 8 yields y = 8
\n" ); document.write( "y = -1/e^-50 + 8 yields y = -5.18..... * 10^21
\n" ); document.write( "y = -1/e^500 + 8 yields overflow
\n" ); document.write( "y = -1/e^-500 + 8 yields divide by 0 error.
\n" ); document.write( "the calculator could handle e ^ plus or minus 50, but it couldn't handle e ^ plus or minus 500 since the resulting number was greater than the maximum value the calculator could handle.
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