Part A
One of the common criteria for
determining relationships that are functions is by evaluating the existence of
distinctive variables operating as inputs and outputs, but with a distinctive
relationship between the inputs and the outputs. A function is a relationship
that has one distinctive variable being mapped to another distinctive variable
by a condition. A function consists of two or more variables that relate to
each other through a mathematical criterion. In such a case, one variable is
said to be a function of the other, so long as there is a condition to the
relationship. For example, a variable, X, can be said to be related to another
variable, Y, if there exists a condition to relate the two. If the condition is
denoted as n, then a function can be
written as, f (x) n= y, or nX=Y.
One of the functions is the compound
interest formula; FV = pv(1+i)^n (Lusardi
and Mitchelli 36)
Where FV
is the Final Value
PV is the Primary Value, i is the
interest rate and n is the period of repayment
The formula is a non-linear function
since the rate of change of the total value with respect to the interest rate
is not the same, but rather an exponential. In linear functions, the rate of
change of the functions must be linear. In the compound interest formula, the
rate of change of variables at any one time changes with a change in one
variable.
The function is a mathematical model
and can be rewritten as;
f (i) = p(1+i)^n
Part B
Relationships
that are non-functions have inconsistent relationships between variables.
Rather than mapping specific variable from another variable through a common
relationship, non-functions have inconsistent relationships.
One of
the non-functions is x^2 + y^2 =200
In this
relationship, one of the variables is assigned different numbers of the
corresponding variable. A relationship is not a function if the condition
equating the values of one variable to the other is inconsistent, or when there
is no relationship to map one variable as a function of the other.
Work
Cited
Lusardi,
Annamaria, and Olivia Mitchelli. "Financial literacy and retirement
preparedness: Evidence and implications for financial education." Business
Economics 42.1 (2007): 35-44.
I really enjoyed how you explained every little detail and identified each value explaining its meaning. However i did not understand which article did you used to prove and show your explanations.
ReplyDeleteVery well written, I do agree with Gabriela though, is this just formula based, or did you dins tables somewhere? In that case, what was the outcome? :)
ReplyDeleteHer is an additional reference material to indicate my source of formulas and explanations. Formula based and there were no graphical representations.
ReplyDeleteClement, Lisa L. “What Do Students Really Know about Functions?” Mathematics Teacher 94.9 (2001): 745-748.
ReplyDeletehashim,
ReplyDeleteyour first example was well explained and you did a good job. your second example is good, as well, however you did not put the function in a real world context which was the purpose of this assignment.
professor little