Answer:
Step-by-step explanation:
To compare the fractions we require them to have a common denominator.
The lowest common multiple of 3 and 7 is 21
Change both fractions into fractions with a denominator of 21
and
= and
The numerator 14 is greater than 12, hence
is the larger fraction
Answer:
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
.
