Question

Which peicewise function is shown in the graph?​

Answer 1

Option (1)

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 =
`(y_2-y_1)/(x_2-x_1)`

=
`(2-1)/(-2-0)`

=
`-(1)/(2)`

Equation of the segment passing through (-2, 2) with slope =
`-(1)/(2)`,

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

`y-2=-(1)/(2)(x+2)`

`y=-(1)/(2)x-1+2`

`y=-(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 =
`(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.