(a) find an equation for the family of linear functions with slope 2 and sketch several members of the family.
(b) find an equation for the family of linear functions such that (2) = 1 and sketch several members ofthe family.
(c) which function belongs to both families?

Step-by-step explanation:

First, we know that family of functions represents a set of functions whose equations have a similar form. In our case, a family of linear functions can be represented as

                                   .

Now, we can take an arbitrary member of that family, a function

for some real constants and .

In this part of the problem, we know that , so we consider

                                    .

To graph several members of the family, you can plug in any real number in the equation above instead of , since satisfy the equation.

For , we have

For , we have .

For , we have

The graphs for the values and are presented on the first graph below.

We need to find the member of the family of linear functions such that

                                   .

Substituting for in gives

                                 .

Now, since we have that , we can equate with and express one of them in terms of the other.  

Substituting for in gives the equation

which represents the wanted family. To sketch several member, we can choose any real value for , since satisfy the equation.  

For , we have .

For , we have

The graph is presented below.

A function belongs to both families if it satisfies both conditions; Its slope must be equal to and .

Let's consider a function

for some real constants and .

The objective is to find the numeric value of the constants and . Since the slope must be equal to , we obtain that and

                               .

To find the numeric value of , we use the fact that .

Substituting for gives

                              .

On the other hand, since , we obtain that

Therefore, a function that belongs to both families is

                                      .

127

whether it's diameter, or radius, i believe if i remember correctly from school, every amount has to always add up to 180. so if you take 53, and starting adding, long story short, taking 127 and adding it to 53, gives you 180.