Question

determine if the following is a function, and if it is a one-to-one function.\\{(0,9),(1,2),(9,2),(3,7),(4,6)\\} \
answer \
\bigcirc not a function \
\bigcirc a function, not one-to-one \
\bigcirc a one-to-one function

Explanation:

Step1: Check if it's a function

A relation is a function if each input (x - value) has exactly one output (y - value). In the set \(\{(0,9),(1,2),(9,2),(3,7),(4,6)\}\), the x - values are \(0,1,9,3,4\). Each x - value appears only once, so each input has exactly one output. So this relation is a function.

Step2: Check if it's one - to - one

A function is one - to - one if each output (y - value) corresponds to exactly one input (x - value). The y - value \(2\) corresponds to two different x - values (\(x = 1\) and \(x=9\)). So the function is not one - to - one.

Answer:

B. A function, not one - to - one