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 functionAs 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, rangeLearn more about piece-wise function from brainly.com/question/12687437#learnwithBrainly