Question

May someone help me out on this question?

Answer 1

y = 2 for x < 0

x for 0 ≤ x < 3

3 for x ≥ 3

Explanation:

From the graph attached,

Equation of line (1),

y = 2

Where x < 0

Let the equation of line (2) is,

y = mx + b

y-intercept 'b' = 0 [line (2) passes through origin]

Slope of the line 'm' =
`\frac{\text{Rise}}{\text{Run}}`

=
`(3)/(3)`

= 1

Therefore, equation of line (2) will be,

y = x

where 0 ≤ x < 3

Equation of line (3) will be,

y = 3

Where x ≥ 3

Therefore, piecewise linear function will be,

y = 2 for x < 0

x for 0 ≤ x < 3

3 for x ≥ 3