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.
