Which piecewise function is shown in the graph?

The piecewise function is shown in the graph is

Step-by-step explanation:

At first, you must find the equation of each line

The form of the equation of the line is f(x) = m x + b, where

From the graph

∵ The line to the left intersects the y-axis at point (0, 1)

∴ b = 1

∵ The line passes through points (0, 1) and (-2, 2)

∴ Δx = -2 - 0 = -2

∴ Δy = 2 - 1 = 1

→ Use them to find the value of m

∵ m = Δy/Δx

∴ m =

∴ m = -0.5

→ Substitute the values of m and b in the form of the equation above

∴ f(x) = -0.5x + 1

∵ The domain of the function is the values of x

∵ The line starts with an empty circle

→ That means x = 0 does not belong to the domain

∴ The sign of inequality is < without equal

∴ The domain of f(x) is x < 0 ⇒ all values less than 0

∵ We have only one answer has f(x) = -0.5x + 1, x < 0

∴ The graph represents the first answer A

∴ The piecewise function is shown in the graph is

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