Answer:
The graph of this piece-wise function is attached below.
Step-by-step explanation:
Given the function
[tex]{\displaystyle f(x)={\begin{cases}x^{2} +2&{\text{if }}-5\leq x<3\\x-4&{\text{if }}3\leq x<7{{}}\text{ }}\g\end{cases}}}[/tex]
- A piece-wise function is a function which has multiple pieces.
- Each of the pieces have their own restrictions.
- The domain of a function is the set of input, or x, values for which the function is defined.
- The range is the set of all values taken by the function
As the piece
[tex]f(x)=x^{2} +2[/tex] has the domain [-5, 3) and graph of this piece is attached below.
and
[tex]f(x)=x-4[/tex] has the domain [3, 7) and graph of this piece is attached below.
So, the domain of the piece-wise function can be composed as [-5, 3) U [3, 7) and range has the interval [tex]\:\left[-1,\:27\right][/tex].
i.e.
Domain: [-5, 3) U [3, 7)
Range: [tex]\:\left[-1,\:27\right][/tex]
The graph of this piece-wise function is attached below.
Keywords: piece-wise function, domain, range
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