Page 187 - ABCTE Study Guide_Neat

Question

All of the followings are functions except:

Answer

The correct answer is C. Choice C is not a function because there are repeated x-values in the table.
Choice D is not a one-to-one function, but it is still a function.

Function Rules

A function rule is an equation that describes a function. A typical function rule looks something like this:

Plug in values for x to get values for y. Sometimes a domain, in set brackets, is given and you are
expected to find the range.

Example

Given the domain {0, 2, 4} and the function rule y = 3x + 2, find the range.

y = 3(0) + 2 = 2

y = 3(2) + 2 = 8

y = 3(4) + 2 = 14

The range for the function rule y = 3x + 2 is {2, 8, 14}.

Sometimes the equation is written with function notation, f(x), instead of y. It means the same thing, but
shows what input value was used to find the output. To read f(x), say f of x. The previous function rule
would look like this: f(x) = 3x + 2.

Real-life situations can sometimes be modeled with functions. Situations where the independent and
dependent variables increase or decrease together and situations where one increases while the other
decreases are often functions.