Question

Which function is graphed below

Answer 1

Explanation:

Graph given for the function has three segments therefore, its a piecewise function.

For a segment lying between (2, ∞)

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

=
`(2)/(1)`

= 2

y-intercept of the line = -2

Therefore, equation of the line will be,

y = 2x - 2

Second segment is a straight line,

Equation of the line will be,

y = 4

Third segment is a straight line.

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

=
`(1)/(1)`

= 1

Equation of the line will be,

y = x + b

Since, this line passes through a point (6, 7)

7 = 6 + b

b = 1

Therefore, equation of the third segment will be,

y = x + 1

So the piecewise function will be,

f(x) = 2x - 2 For x < 2

4 For 2≤ x ≤ 5

x + 1 For x > 5