is really a family of equations, because for each value of k, we get a different equation with the unknown x. The letter k is called a parameter for this family. What value should we pick for k to make the given value of x a solution of the resulting equation

Follows are the solution to this question:

Step-by-step explanation:

please find the complete question in the attached file:

In view of their choices, they could solve this problem by linking x and k finding values that meet the value.  

a) In the family for equations they have, the plugin first x value.

It is also obvious that k = 3 makes x = 0 for that equation family.  

b) See now the second x value:

It is also obvious that k=3 renders a solution for this equation family of x=1.

c)

We plug in the 3rd of x, finally.

So k could be any real value and x=2 could be a solution for the equations family.  

a) 3

b) 3

c) Any real value