Question

students were asked to create a representation of y as a function of x. circle the names of the students who correctly completed the task. then, unscramble the underlined letters of the circled names to answer the question at the bottom. charlotte sofia deshaun jace nathan coldy abby orlando stephanie what is the only number whose letters are in alphabetical order?

Explanation:

Step1: Recall function - definition

A relation is a function if for each input \(x\) - value, there is exactly one output \(y\) - value.

Step2: Analyze Charlotte's graph

The graph passes the vertical - line test (a vertical line drawn anywhere on the graph intersects the graph at most once), so it represents a function.

Step3: Analyze Sofia's mapping

The input \(x = 6\) has two outputs (\(y = 6\) and another \(y\) - value), so it is not a function.

Step4: Analyze Deshaun's set of ordered pairs

The input \(x=-6\) has two outputs (\(y = 7\) and \(y = 11\)), so it is not a function.

Step5: Analyze Jace's mapping

The input \(x = 5\) has two outputs (\(y = 6\) and \(y=-6\)), so it is not a function.

Step6: Analyze Nathan's table

For each \(x\) - value in the table, there is exactly one \(y\) - value, so it represents a function.

Step7: Analyze Colby's graph

The graph fails the vertical - line test (a vertical line can intersect the graph more than once), so it is not a function.

Step8: Analyze Abby's graph

The graph fails the vertical - line test (a vertical line can intersect the graph more than once), so it is not a function.

Step9: Analyze Orlando's set of ordered pairs

For each \(x\) - value in the set \(\{(9, - 2),(7,5),(4,-3),(-9,6)\}\), there is exactly one \(y\) - value, so it represents a function.

Step10: Analyze Stephanie's table

The input \(x=-4\) has two outputs (\(y = 6\) and \(y=-6\)), so it is not a function.

Step11: Unscramble the underlined letters

The students who correctly represented \(y\) as a function of \(x\) are Charlotte, Nathan, and Orlando. The underlined letters are 'R', 'T', 'N', 'O'. Unscrambling them gives 'TORN'. But we need to answer the number question. The only number whose letters are in alphabetical order is 'forty'.

Answer:

forty