What do both of these functions have in common? f(x)=3/2|x-7|-2 g(x)=1.5in(x-2)+7

Option: B is the correct answer.

B.  They have the same vertical stretch.

We are given function f(x) as:

and function g(x) as:

As we know that for any function of the type:

        f(x)=a f(x)

if a>1 then the transformation would be a vertical stretch.

and if 0<a<1 then the transformation is a vertical shrink.

In the given function we see that the function f(x) has a vertical stretch of 3/2=1.5 units and the function g(x) has a vertical stretch of 1.5 units.

Hence, both the functions f(x) and g(x) have the same vertical stretch.

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.

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step-by-step explanation: