Question

Which of the following piecewise functions is represented in the graph below? 7 f 2 -1 -1 Previous Next

it is actually algebra not econmic. i selected wrong by accident!

Answer 1

Solution:

Given the graph, for range x < -2, we can pick any point coordinates to see how function is behaving.

Firstly it is linear, so x will have power of 1. Now let's take up for example, point (-3, 4) that is x = -3, and f(x) = 4

So, f(x) = 1 - x works here: 4 = 1 - (-3) => 4 = 4 is satisfied

We can pick one more coordinate point to verify the function: (-6, 7), so, 1 - x = 1 - (-6) = 7 = f(x)

Similarly, for range x > 1, the function is linear and we can pick any point co-ordinates to verify the function: (3, 0) that is x = 3, f(x) = 0

So, f(x) = x - 3 seems to work here. (similarly, we can pick up one more point from x > 1 point coordinate to verify the function, as for a single point, multiple linear functions can support)

Thus, the correct option is (A).

Please note that another way of working through it for the linear function part (that is for x < -2, and x >1) is using straight line derivation from two points.