Question

Select each correct answer.

f(x) is a polynomial function.

f(x) is an exponential function.

g(x) is a polynomial function.

g(x) is an exponential function.

The output values of f(x) will remain greater than those of g(x) as the input values continue to increase.

The output values of g(x) will surpass those of f(x) as the input values continue to increase.

Answer 1

By examining the table of ordered pairs, notice that the function f(x) is the cube of
`x`. Therefore,
`f(x)=x^3`

By examining the table of ordered pairs, notice that as
`x` increases by a constant value, the value of the function g(x) increases by the common ratio of 3. Therefore,
`g(x)=3^x`

From the table, both functions equal 27 when
`x=3`, therefore, the point of intersection of the two functions is (3, 27).

As x increases past
`x=3`, g(x) increases quicker than f(x) since g(x) is an exponential function and f(x) is a cubic polynomial.

So the following statements are true:

• f(x) is a polynomial function
• g(x) is an exponential function
• The output values of g(x) will surpass those of f(x) as the input values continue to increase.

Please refer to the attached graph of both functions with plotted ordered pairs.

Answer 2

• f(x) is a polynomial function.

• g(x) is an exponential function.

• The output values of g(x) will surpass those of f(x) as the input values continue to increase.

Step-by-step explanation:

• f(x) has a function of x³

• g(x) has a function of
  `\sf 3^X`

False statements:

• The output values of f(x) will remain greater than those of g(x) as the input values continue to increase.

• f(x) is an exponential function - as crosses x-axis, exponential never crosses x-axis

• g(x) is a polynomial function - as has no valid power.