Question

Graph the following piecewise function.

Answer 1

Answer:

The graph of this piece-wise function is attached below.

Step-by-step explanation:

Given the function

${\displaystyle f(x)={\begin{cases}x^{2} +2&{\text{if }}-5\leq x$

• 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

$f(x)=x^{2} +2$ has the domain [-5, 3) and graph of this piece is attached below.

and

$f(x)=x-4$ 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 $\:\left[-1,\:27\right]$.

i.e.

Domain: [-5, 3) U [3, 7)

Range: $\:\left[-1,\:27\right]$

The graph of this piece-wise function is attached below.

Keywords: piece-wise function, domain, range

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