SOLUTION: A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function? graph of function g of x is a curve which joins th

Question 940762: A quadratic function and an exponential function are graphed below. Which graph most likely represents the exponential function?
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
1. f(x), because an increasing quadratic function will eventually exceed an increasing exponential function.
2. g(x), because an increasing exponential function will eventually exceed an increasing quadratic function.
3. f(x), because an increasing exponential function will always exceeds an increasing quadratic function until their graphs intersect.
4. g(x), because an increasing quadratic function will always exceeds an increasing exponential function until their graphs intersect.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
g(x) is the exponential function (in this case g(x) = 2^x), but 2. is more correct.

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).

4. is true for this quadratic, but not true in general.
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