Question

Explain how to graph the given piecewise-defined function. Be sure to specify the type of endpoint each piece of the function will have and why. f(x) = { -x + 3, x < 2, 3, 2 < x < 4, 4 - 2x, x > 4

Answer 1

You would graph the equation f(x) = –x + 3 for input values less than 2. There would be an open circle at the point (2, 1) since the domain for the first piece does not include 2. You would then graph a horizontal line at f(x) = 3 for input values between 2 and 4. There would be a closed circle at (2, 3) and an open circle at (4, 3). Last, you would graph f(x) = 4 – 9x for input values greater than or equal to 4. There would be a closed circle at the point (4, –4) since 4 is in the domain of the third piece.

Answer 2

Our piecewise-defined function consist of three sub functions.

The first one is

-x+3, for domain x<2

if we put 2, -2+3=1 so at (2,1) function is not defined and we have empty circle at this point.

The second one is

3, for the domain 2<x<4

3 is a constant function for the domain 2<x<4 and not defined at x=2 and x=4, open circle at both points.

The third one is

4-2x, for the domain x>4

if we put 4, 4-2(4)=-4 so at (4,-4) function is not defined and we have empty circle at this point.

So,

our piecewise defined function is discontinuous.

The graph is attached below.