document.write( "Question 940762: A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function?
\n" ); document.write( "graph of function g of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 8 and 5, 32 and 6, 64. Graph of function f of x is a curve which joins the ordered pair 0, 1 and 1, 2 and 3, 10 and 5, 26 and 6, 37\r
\n" ); document.write( "\n" ); document.write( "1. f(x), because an increasing quadratic function will eventually exceed an increasing exponential function.
\n" ); document.write( "2. g(x), because an increasing exponential function will eventually exceed an increasing quadratic function.
\n" ); document.write( "3. f(x), because an increasing exponential function will always exceeds an increasing quadratic function until their graphs intersect.
\n" ); document.write( "4. g(x), because an increasing quadratic function will always exceeds an increasing exponential function until their graphs intersect. \n" ); document.write( "

Algebra.Com's Answer #573549 by richard1234(7193) $\"\"$ $\"About$

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g(x) is the exponential function (in this case g(x) = 2^x), but 2. is more correct.\r
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\n" ); document.write( "\n" ); document.write( "2. If we interpret \"eventually exceed\" as \"x increases to +infinity\", then this statement is always true for increasing exponential functions. For example, if f(x) = 100000x^2 and g(x) = 1.0001^x, then g(x) will eventually overtake f(x). In asymptotic notation, we write

, i.e. f(x) is asymptotically smaller than g(x).\r
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\n" ); document.write( "\n" ); document.write( "4. is true for this quadratic, but not true in general. \n" ); document.write( "

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