Question

identifying functions
students were asked to create a representation of y as a function of x. circle the names of the
udents who correctly completed the task. then, unscramble the underlined letters of the circled
ames to answer the question at the bottom.
charlotte
sofia
deshaun
{(-6,7),(-1,4),(2,9),(-6,11)}
jace
nathan
colby
abby
orlando
stephanie
what is the only number whose letters are in alphabetical order?

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input \(x\) - value has exactly one output \(y\) - value.

Step2: Analyze Charlotte's graph

Using the vertical - line test (a vertical line drawn anywhere on the graph should intersect the graph at most once). Charlotte's graph passes the vertical - line test.

Step3: Analyze Sofia's mapping

Each \(x\) - value (\(-6\), \(6\), \(20\), \(36\)) maps to exactly one \(y\) - value (\(-6\)).

Step4: Analyze Deshaun's set of ordered pairs

The \(x\) - value \(-6\) maps to two different \(y\) - values (\(7\) and \(11\)), so it is not a function.

Step5: Analyze Jace's mapping

The \(x\) - value \(5\) maps to two different \(y\) - values (\(6\) and \(-6\)), so it is not a function.

Step6: Analyze Nathan's table

Each \(x\) - value (\(-4\), \(0\), \(5\), \(11\)) has exactly one \(y\) - value (\(-8\), \(-13\), \(-4\), \(14\)).

Step7: Analyze Colby's graph

The graph fails the vertical - line test (a vertical line through the origin intersects the graph infinitely many times), so it is not a function.

Step8: Analyze Abby's graph

The graph fails the vertical - line test (a vertical line through the \(y\) - axis intersects the graph infinitely many times), so it is not a function.

Step9: Analyze Orlando's set of ordered pairs

Each \(x\) - value (\(9\), \(7\), \(4\), \(-9\)) has exactly one \(y\) - value (\(-2\), \(5\), \(-3\), \(6\)).

Step10: Analyze Stephanie's table

The \(x\) - value \(-4\) maps to two different \(y\) - values (\(6\) and \(-6\)), so it is not a function.

The circled names are Charlotte (\(C\)), Sofia (\(S\)), Nathan (\(N\)), Orlando (\(O\)). Unscrambling the underlined letters \(C\), \(S\), \(N\), \(O\) gives \(C - O - N - S\).

Answer:

\(C - O - N - S\) (which is the number \(19\) in a non - standard way, but if we consider the letters from the names of the students who made functions: Charlotte (\(C\)), Sofia (\(S\)), Nathan (\(N\)), Orlando (\(O\)) and assume a simple mapping \(A = 1,B = 2,\cdots,Z=26\), \(C = 3\), \(O = 15\), \(N = 14\), \(S=19\). But if we consider the riddle "What is the only number whose letters are in alphabetical order", the answer is \(40\) (forty: \(f(6),o(15),r(18),t(20),y(25)\) are in alphabetical order)