Answer:
Step-by-step explanation:
Graph given for the function has three segments therefore, its a piecewise function.
For a segment lying between (2, ∞)
Slope of the line =
=
= 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 =
=
= 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