The equation of the piecewise function is [tex]f(x) = \left[\begin{array}{ccc}3&x \le -1\\-1&x > 2\end{array}\right[/tex]
The piecewise function
On the graph, we have:
- y = 3 for all x values not more than -1
- y = -1 for all values greater than 2
Hence, the piecewise function is:
[tex]f(x) = \left[\begin{array}{ccc}3&x \le -1\\-1&x > 2\end{array}\right[/tex]
The domain of the function
This is the set of input values
In (a), we have:
x ≤ -1 and x > 2
Hence, the domain is (∞, 3] u (2, ∞)
The range of the function
This is the set of output values
In (a), we have:
f(x) = 3 and f(x) -1
Hence, the range is [3] u (-1)
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