Question

What function represents this graph??

Answer 1

The required piecewise function that represents the graph is given as:

$f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.$

Piecewise functions

The graph consists of 3 lines with different equations and slopes. In order to determine the function it represents, we will create a piecewise function.

For the line crossing the negative x-axis

Using the coordinate points (-4, 2) and (-2, -4)

Slope = -6/2

Slope = -3

2 = -3(-4) + b
2 - 12 = b

b = -10

The equation of the line will be y = -3x-10

For the line crossing the negative y-axis

Using the coordinate points (-2, -4) and  (2,-2)

Slope = 2/4

Slope = 1/2

-2 = 1/2(2) + b
-2 - 1 = b

b = -3

The equation of the line will be y = -1/2x-3

For the line crossing the positive x-axis

Using the coordinate points (2, -2) and (3, 0)

Slope = 2/1

Slope = 2

0 = 2(3) + b
0 - 6 = b

b = -6

The equation of the line will be y = 2x-6

The required piecewise function that represents the graph is given as:

$f(x)=\left \{ {{y = -3x-10} \atop y=-\frac{1}{2}x-3 } \atop y=-2x-6 }} \right.$

Learn more on piecewise function here: brainly.com/question/18499561

#SPJ1