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
{(-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 function - definition

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

Step2: Analyze Charlotte's graph

The graph represents a set of points. By the vertical - line test, if we can draw a vertical line that intersects the graph at more than one point, it is not a function. This graph represents a function as no vertical line will intersect it at more than one point.

Step3: Analyze Sofia's mapping

The input value of - 6 has two output values, so it is not a function.

Step4: Analyze Deshaun's set of ordered pairs

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

Step5: Analyze Jace's mapping

The input value of 5 has two output values (6 and - 6), so it is not a function.

Step6: Analyze Nathan's table

Each x - value has exactly one y - value, so it is a function.

Step7: Analyze Colby's graph

The graph fails the vertical - line test (it is a vertical line), so it is not a function.

Step8: Analyze Abby's graph

The graph is just the x and y axes, not a proper graph of a function. It fails the vertical - line test in most places.

Step9: Analyze Orlando's set of ordered pairs

Each x - value has exactly one y - value, so it is a function.

Step10: Analyze Stephanie's table

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

Step11: Identify correct students

The students who correctly represented y as a function of x are Charlotte, Nathan, and Orlando.

Step12: Unscramble letters

The underlined letters from Charlotte, Nathan, and Orlando are L, T, N. Unscrambling them gives the word "TEN".

Answer:

TEN