Question

Hi I need help with this review question.Which set of ordered pairs in the form of (x, y) does NOT represent a function of x?

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given function.

STEP 2: Define a function

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

From this definition, we can imply that one element of set X must only give you exactly one element from set Y. There can be multiple values for y though.

STEP 3: Check the given option for pairs that have multiple values for x

OPTION A:

`\begin{gathered} x-values:-1,3,0,5 \\ y-values:2,2,1,2 \\ \\ There\text{ are unique values for x} \end{gathered}`

OPTION B

`\begin{gathered} x-values:-1,3,-2,0 \\ y-values:2,2,2,2 \\ \\ There\text{ are unique values for x} \end{gathered}`

OPTION C

`\begin{gathered} x-values:-1,3,0,3 \\ y-values:2,-2,1,5 \\ \\ There\text{ are no unique values for x as one value of 3 gives two outcomes of -2 and 5} \end{gathered}`

OPTION D:

`\begin{gathered} x-values:-1,2,3,-2 \\ y-values:2,3,2,0 \\ \\ There\text{ are unique values for x} \end{gathered}`

Hence, the set of ordered pairs that does not represent a function of x is:

OPTION C