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The piecewise function g(x) is shown in the graph.

Graph with three pieces. The first piece is a horizontal line from the left with an open right endpoint at negative 2 comma 2. The second piece is curved with a solid point at negative 2 comma 0, which passes through negative 1 comma 1, and it ends at 0 comma 4 with a solid circle. The last piece starts with an open circle at 0 comma 4 and decreases to the right as it passes through 4 comma 0.

Which of the following represents g(x)?

The piecewise function gx is shown in the graph Graph with three pieces The first piece is a horizontal line from the left with an open right endpoint at negati class=
The piecewise function gx is shown in the graph Graph with three pieces The first piece is a horizontal line from the left with an open right endpoint at negati class=

Respuesta :

MrRoyal

The equation for the piecewise function graphed below is

g(x) = 2 if x < -2

g(x) = (x + 2)^2 if -2 <= x <= 0

g(x) = -x + 4 if x > 0

How to complete the equation of the piecewise function graphed below?

On the interval -∝ < x < -2

There is a horizontal line that passes through y = 2

So, we have:

g(x) = 2 if -6 -∝ < x < -2

On the interval -2 <= x <= 0

There is a curve that has an equation y = (x + 2)^2

So, we have:

g(x) = (x + 2)^2 if -2 <= x <= 0

On the interval x > 0

There is a line that has an equation y = -x + 4

So, we have:

g(x) = -x + 4 if x > 0

Hence, the equation for the piecewise function graphed below is

g(x) = 2 if x < -2

g(x) = (x + 2)^2 if -2 <= x <= 0

g(x) = -x + 4 if x > 0

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