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

Which values are with in the range of the piecewise defined function?-example-1
User Hexxefir
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1 Answer

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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

  • 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)

User Budric
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