Question

Which function is graphed below

Answer 1

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 = $\frac{\text{Rise}}{\text{Run}}$

                            = $\frac{2}{1}$

                            = 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 = $\frac{\text{Rise}}{\text{Run}}$

                            = $\frac{1}{1}$

                            = 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