Question

Which peicewise function is shown in the graph?​

Answer 1

Answer:

Option (1)

Step-by-step explanation:

From the graph of the piecewise function,

There are two pieces of the function,

1). Segment (1) having x < 0

2). Segment (2) having x ≥ 0

Segment (1),

Segment starts with a hollow circle at x = 0 and passes through two points (0, 1) and (-2, 2)

Slope of the segment = $\frac{y_2-y_1}{x_2-x_1}$

                                     = $\frac{2-1}{-2-0}$

                                     = $-\frac{1}{2}$

Equation of the segment passing through (-2, 2) with slope = $-\frac{1}{2}$,

$y-y'=m(x-x')$

$y-2=-\frac{1}{2}(x+2)$

$y=-\frac{1}{2}x-1+2$

$y=-\frac{1}{2}x+1$

$y=-0.5x+1$ For x < 0

Segment (2),

Segment starts with a solid circle at x = 0 and passes through (0, -2) and (2,2)

Slope of the segment = $\frac{2+2}{2-0}$

                                    = 2

Equation of the segment passing through (0, -2) and slope = 2,

y - y' = m(x - x')

y + 2 = 2(x - 0)

y = 2x - 2 For x ≥ 0

Therefore, Option (1) will be the correct option.