Respuesta :

A piecewise function is one that has different operations, depending on the values of the input

The piecewise function is;

[tex]g(x) = \begin{cases} -\left | x + 2 \right |&\mathbf{ \text{ if } -5 \leq x < 0 }\\ 2 \cdot x - 2 &\mathbf{ \text{ if } 0 < x \leq 2}\\ 2 &\mathbf{ \text{ if } 2 \leq x \leq 5}\end{cases}[/tex]

Reason:

The general form of the absolute value function is presented as follows;

[tex]f(x) = \mathbf{a \left | x - h \right | + k}[/tex]

The function given in the graph are;

Domain; -5 ≤ x < 0

Function;  [tex]g(x) = -\left | x + 2 \right |[/tex]

Domain; 0 < x ≤ 2

Points on the graph are;

(0, -2), and (2, 2)

Slope = (2 - (-2))/(2 - 0) = 2

g(x) - (-2) = 2·(x - 0)

∴ Function; g(x)  = 2·x - 2

Domain; 2 ≤ x ≤ 5

Function; g(x) = 2

Therefore, we have the following piecewise function;

[tex]g(x) = \mathbf{ \begin{cases} -\left | x + 2 \right |& \text{ if } -5 \leq x < 0 \\ 2 \cdot x - 2 & \text{ if } 0 < x \leq 2\\ 2 & \text{ if } 2 \leq x \leq 5\end{cases}}[/tex]

Learn more about piecewise functions here:

https://brainly.com/question/12700276

https://brainly.com/question/3860983

https://brainly.com/question/16855064

LammettHash

See attached for the graphs of the various transformations of g(x).

• g(x) + 1 is a vertical shift upward by one unit

• g(x - 1) is a horizontal shift to the right by one unit

• -g(x) is a reflection across the x-axis

• 2g(x) is a scaling by a factor of 2

• -g(x - 1) is the composition of g(x - 1) and -g(x), hence a reflection and a horizontal shift

• |g(x)| leaves the positive parts of g(x) alone, and negates the negative parts (in other words, the parts of the graph of g(x) below the x-axis are reflected, the rest stays the same)

Ver imagen LammettHash

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