Answer:
The range of the piecewise defined function is:
y= -6 , y= -4 , y= -3 , y=0
Explanation:
The piecewise function is defined by:
f(x) = 2x+2 when x < -3
x when x = -3
and -x-2 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
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)