Answer:
The piecewise function is shown in the graph is
- f(x) = -0.5x + 1, x < 0
- 2x - 2, x ≥ 0 ⇒ A
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
- m is the slope of the line which = Δy/Δx
- b is the y-intercept which is the y-coordinate of the point of intersection between the line and the y-axis
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 = [tex]\frac{1}{-2}[/tex]
∴ 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
- f(x) = -0.5x + 1, x < 0
- 2x - 2, x ≥ 0
