Student Press: Survey Pair Checks

Decide when survey records define a function.

Check the Survey Records

The school newspaper is surveying student opinions. For each relation, use the stated input and output. Judge only the records shown.

Each surveyed student has a unique ID. The input is student ID, and the output is the student's preferred article topic. Does this table define a function?

Article Preferences
Student ID	Preferred topic
201	School news
202	Reviews
203	School news
204	Interviews

A. Yes; every student ID has one topic.B. No; two students chose the same topic.C. No; the outputs must all be numbers.D. Yes; every topic has one student ID.

The input is grade level, and the output is a student's preferred survey format. Which input has two different outputs?

Survey Format Preferences
Grade level	Preferred format
6	Paper
7	Online
8	Online
7	Paper

The input is .

An editor makes a new rule: input an article topic, and output the number of students who chose it. Does this rule define a function?

Topic Totals
Article topic	Number of students
School news	18
Reviews	12
Interviews	12
Opinion	15

A. Yes; each topic has exactly one count.B. Yes; each count has exactly one topic.C. No; two topics have the same count.D. No; a topic cannot be an input.

Sort these proposed survey rules. Each student's ID identifies exactly one student.

The input is student ID, and the output is an interest rating. Which single row could be added without making the relation fail to be a function?

Interest in a New Opinion Column
Student ID	Interest rating
411	2
412	4
413	2

A. Add student ID 413 with rating 5.B. Add student ID 414 with rating 2.C. Add student ID 412 with rating 1.D. Add student ID 411 with rating 3.

Read the Plotted Opinions

Opinion codes are −2 (strongly oppose), −1 (oppose), 0 (neutral), 1 (support), and 2 (strongly support). Each graph contains only the plotted pairs; do not connect the points.

The input is a student's code for a longer lunch period. The output is that student's code for a later school start. What output is paired with input −1?

The output is .

Use the graph in Question 6. Which statement correctly describes its set of pairs?

A. It is a function because each plotted output has one input.B. It is not a function because some coordinates are negative.C. It is a function because each plotted input has one output.D. It is not a function because P and S share an output.

Here the input is an opinion code for quiet lunch spaces, and the output is a code for outdoor lunch spaces. Which pair of points shows that the output is not a function of the input?

A. Points A and D show the conflict.B. Points A and B show the conflict.C. Points B and C show the conflict.D. Points C and D show the conflict.

The graph below defines a function from print-edition opinion code to online-edition opinion code. Select every new pair that could be added individually while keeping it a function.

Make the Editor's Decisions

Apply the function definition to new survey tasks. Pay attention to which quantity is the input.

10.

The newspaper turns an interest rating into a follow-up question count. Ratings 1 and 2 each give 1 question; rating 3 gives 2 questions; ratings 4 and 5 each give 3 questions. Which graph contains exactly this rule's input-output pairs?

A. {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5)}B. {(1, 1), (2, 1), (3, 2), (4, 3), (5, 3)}C. {(1, 1), (1, 2), (2, 3), (3, 4), (3, 5)}D. {(1, 1), (2, 1), (3, 2), (4, 3), (5, 2)}

11.

The editor wants the following pairs to define a function. The input is interest rating, and the output is the number of follow-up questions. What number must replace the question mark?

Follow-Up Records
Interest rating	Follow-up questions
1	0
3	2
5	4
3	?

The missing output must be .

12.

A survey chart has input-output pairs (1, 4), (2, 4), (3, 4), and (4, 4). The input is interest rating; the output is the recommended number of article choices to show. Which description of its graph is correct?

A. Four points share y-coordinate 4, so it is not a function.B. Four points share x-coordinate 4, so it is not a function.C. Four points share x-coordinate 4, so it is a function.D. Four points share y-coordinate 4, so it is a function.

13.

The editor records these pairs as (student ID, opinion code): (521, 1), (522, −1), (523, 1). This relation is a function. Noor says that reversing every pair must also give a function because no survey information changes. Is Noor correct? Use the reversed pairs to explain your reasoning.