**Sample Essay**

*Which of the following are functions? Explain your reasoning for a, b, and c. *

*Keep the definition of a function strongly in mind as you do this problem, it is not nearly as difficult as it may look. Think about whether the relationship between f(x) and x is consistent with being a function or not and explain your reasoning. Problems b & c are multi part relations so consider all parts when deteriming if they are funcitons.*

*a. f(x) = x 8 *

*b. f(x) = 45 if x>2 otherwise f(x) = -4 *

*c. f(x) = 4 if x>0 or f(x) = -4 if x<0 or f(x) = 4 or -4 if x = 0 *

A function is a relation between two variable whose values varies according to a certain proportion. Hence by this definition part a is a function because the value of f(x) will vary according to x. Part b has the same case and is a function. In part c the value of f(x) does not vary according to proportion of x hence both are not functions (Algebra, 2010).

*8 For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function. Explain your reasoning thoroughly.*

*a. The time it takes you to get to work as a function the speed at which you drive *

*b. The probability of getting into a car accident as a function of the speed at which you drive *

*c. A person\’s height as a function of the person\’s age (from age 0 to 100) *

Part a is non-linear function because speed and time are inversely related variables. Part b is non-linear however its value depends upon a number of other factors as well. Part c is a non-linear function as the height vs age ratio varies from person to person (Algebra, 2010).

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