Question

How do you model a situation in which a function behaves differently over different parts of its domain?

Answer 1

The situation in which a function behaves differently over different parts of its domain is modeled by considering it to be a piecewise function.

Such a situation can be explained through an example:

f(x)=   { 2x, for x > 0

         {     1, for x = 0

         { -2x, for x < 0

now, when we take x value less than 0, say x= -1

    thus, f(x)= f(-1)= -2(-1) = 2 , here we used f(x) given x<0

now, when we take x value more than 0, say x= 2

    thus, f(x)= f(1)= 2(1) = 2, here we used f(x) given x>0

now, when we take x =  0,

    thus, f(x)= f(0)= 1, here we used f(x) given x=0

this is how we model picewise function, we  use f(x) as per the value of x. Following image shows plotted answer for this example.

Since inequalities given are exclusive of 0, we leave the dot at the origin unfilled. Now, for x = 0. Since the value is constant at f(x) =1, we plotted a point at (0,1)

more questions on picewise functions brainly.com/question/12089993

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