Question

Which values are with in the range of the piecewise defined function?

Answer 1

Answer:

The range of the piecewise defined function is:

                  y= -6 , y= -4 , y= -3 , y=0

Step-by-step explanation:

The piecewise function is defined by:

f(x)  =    2x+2   when  x < -3

              x       when  x = -3

  and  -x-2      when  x > -3

• when x < -3

Then the graph of the function is a strictly increasing function and is a line with a slope of 2.

The function increases continuously from -∞ to -4

i.e. it takes all the value in the interval (-∞,-4)

There is a open circle at (-3,-4)

• Also, at x= -3 the value of function is : -3

• For x > -3

The graph of the function f(x) is strictly decreasing .

Since the graph is a line with slope -1.

Also, there is a open circle at (-3,1)

and the function starts decreasing continuously and will take all the values strictly less than 1.

i.e. the range for x > -3 is:  (-∞,1)

The range of the whole function f(x) is:

                            (-∞,1)

Answer 2

Answer:

y = -6; -3;  0

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x)  = 2x+2  , x < -3

f(x) = x, x = -3

f(x) = - x -2 , x > -3

From the graph, we can see that the values are

y = -6; -3;  0