Use the tables to determine which function will eventually exceed the other, and provide your reasoning. x f(x)−1 −5 0 −6 1 −5 2 −2 x g(x)−1 0.166 0 1 1 6 2 36 f(x) will eventually exceed g(x) because f(x) is an exponential function. f(x) will eventually exceed g(x) because f(x) has a higher rate of change. g(x) will eventually exceed f(x) because g(x) is an exponential function. g(x) will eventually exceed f(x) because g(x) has a higher rate of change.

Answer:g(x) will eventually exceed f(x) because g(x) is an exponential function.Step-by-step explanation:From the first table we can observe the following patterns:[tex]f( - 1) = {( - 1)}^{2} - 6 = - 5[/tex][tex]f(0) = {( 0)}^{2} - 6 = - 6[/tex][tex]f( 1) = {( -1)}^{2} - 6 = - 5[/tex][tex]f(2) = {( 2)}^{2} - 6 = - 2[/tex]In general,[tex]f(x) = {x}^{2} - 6 [/tex]From the second table we can observe the following pattern:[tex]g( - 1) = {6}^{ - 1} = \frac{1}{6} [/tex][tex]g(0) = {6}^{ 0} = 1[/tex][tex]g(1) = {6}^{1} = 6[/tex][tex]g(2) = {6}^{2} = 36[/tex]In general,[tex]g( x) = {6}^{ x} [/tex]Conclusion:Since the f(x) represents a quadratic function and g(x) represents an exponential function, g(x) will eventually overtake f(x).The correct answer is C.