Question

Which function is graphed below?

Answer 1

Piecewise function;

y = 2x - 2 where x < 2

4 where 2 ≤ x ≤ 5

y = x + 1 where x > 5

Explanation:

Function graphed represents the piecewise function.

1). Equation of the line with y-intercept (-2) and slope 'm'.

Since, slope of the line =
`\frac{\text{Rise}}{\text{Run}}`

=
`(2)/(1)`

= 2

Therefore, equation of this segment will be in the form of y = mx + b,

⇒ y = 2x - 2 where x < 2

2). Equation of a horizontal line,

y = 4 where 2 ≤ x ≤ 5

3). Equation of the third line in the interval x > 5

Let the equation of the line is,

y = mx + b

Where m = slope of the line

b = y-intercept

Here, slope 'm' =
`\frac{\text{Rise}}{\text{Run}}`

=
`(2)/(2)`

= 1

Equation of this line will be,

y = 1(x) + b

y = x + b

Since, this line passes through (5, 6),

6 = 5 + b

b = 6 - 5 = 1

Therefore, equation of this line will be,

y = x + 1 where x > 5

Graphed piecewise function is,

y = 2x - 2 where x < 2

4 where 2 ≤ x ≤ 5

y = x + 1 where x > 5