Question

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The table below represents the function f(x).


x 0 2 4 6 8 10 12

f(x) 4.1 5.3 6.5 7.7 8.9 10.1 11.3


If g(x) is a linear function that contains the points (6, -2) and (3, 7), which statement is true?

A.

As x approaches positive infinity, f(x) and g(x) both approach negative infinity.


B.

As x approaches positive infinity, f(x) and g(x) both approach positive infinity.


C.

As x approaches positive infinity, f(x) approaches positive infinity, and g(x) approaches negative infinity.


D.

As x approaches positive infinity, f(x) approaches negative infinity, and g(x) approaches positive infinity.

Answer 1

Option C. As x approaches positive infinity, f(x) approaches positive infinity, and g(x) approaches negative infinity.

Explanation:

we know that

Observing the table

The function f(x) is a increasing function

As the value of x increases, the value of f(x) increases

so

As x approaches positive infinity, f(x) approach positive infinity

Find the slope of the linear equation g(x)

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

we have the points (6, -2) and (3, 7)

substitute

`m=(7+2)/(3-6)`

`m=(9)/(-3)=-3`

The slope of the linear equation g(x) is negative

That means ----> Is a decreasing function

As the value of x increases, the value of g(x) decreases

so

As x approaches positive infinity, g(x) approach negative infinity

therefore

As x approaches positive infinity, f(x) approaches positive infinity, and g(x) approaches negative infinity.