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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

HELP SEE ATTACHED 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 class=

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Step-by-step explanation:

The given expression is

[tex]\frac{f(b)-f(a)}{b-a}=2[/tex]

Notice that [tex]a[/tex] and [tex]b[/tex] are elements of the domain and [tex]f(a)[/tex] and [tex]f(b)[/tex] are elements of the range.

Observe the notation used,  an element of the range is always written like [tex]f(x)[/tex] where [tex]x[/tex] is an element of the domain.

Also, notice that this expression is using two pair of coordinates, which are [tex](a, f(a))[/tex] and [tex](b,f(b))[/tex].

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

[tex]r=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]

Where [tex](x_{1} ,y_{1} )=(a ,f(a))[/tex] and [tex](x_{2} ,y_{2} )=(b ,f(b))[/tex].

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.

Answer:

The average rate of change for the function on the interval [a,b] is 2

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