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if f is a function such that the quotient of the quantity f of b minus f of a and the quantity b minus a equals 2, then which of the following statements must be true?

f(a) = f(b) = 2
the slope of the tangent line to the function at x = a is 2.
the average rate of change of the function on the interval [a, b] is 2
the linear approximation for f(x) at x = a is y = 2

Step-by-step explanation:

The given expression is

Notice that and are elements of the domain and and are elements of the range.

Observe the notation used,  an element of the range is always written like where is an element of the domain.

Also, notice that this expression is using two pair of coordinates, which are and .

On the other hand, the definition of average rate of change is

Where and .

Having said that, the given expression represents an average rate of change in the interval, where the rate is 2. The right answer is the third option.