Question

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 1

Answer: C.

Explanation:

Go it right on my test

Answer 2

g(x) will eventually exceed f(x) because g(x) is an exponential function.

Explanation:

From the first table we can observe the following patterns:

`f( - 1) = {( - 1)}^(2) - 6 = - 5`

`f(0) = {( 0)}^(2) - 6 = - 6`

`f( 1) = {( -1)}^(2) - 6 = - 5`

`f(2) = {( 2)}^(2) - 6 = - 2`

In general,

`f(x) = {x}^(2) - 6`

From the second table we can observe the following pattern:

`g( - 1) = {6}^( - 1) = (1)/(6)`

`g(0) = {6}^( 0) = 1`

`g(1) = {6}^(1) = 6`

`g(2) = {6}^(2) = 36`

In general,

`g( x) = {6}^( x)`

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.