Math Problem Statement

Does this table represent a function? Why or why not? | x | y | |---|---| | 4 | 0 | | 7 | 5 | | 8 | 5 | | 8 | 8 | | 10 | 9 |

Solution

Let's analyze the question.

A table represents a function if every x-value corresponds to exactly one y-value (no x-value is repeated with a different y-value).

Given Table:

xy
40
75
85
88
109

From the table:

  • The x-value 8 is repeated, but it corresponds to two different y-values: 5 and 8.

This violates the rule for functions that says each x-value must pair with only one y-value. Hence, this table does not represent a function.

Correct Answer:

D. No, because one x-value corresponds to two different y-values.


Would you like me to explain this in more detail or clarify further?

Here are 5 related questions for deeper understanding:

  1. What is the definition of a function in terms of x- and y-values?
  2. How can you quickly identify whether a table represents a function?
  3. What is the difference between a function and a relation?
  4. Can two different x-values correspond to the same y-value in a function? Why?
  5. How would this concept apply to a graph representation?

Tip: A quick way to check for functions is the vertical line test for graphs or ensuring no x-values repeat with different y-values in tables.

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Math Problem Analysis

Mathematical Concepts

Functions
Relations
Algebra

Formulas

A relation is a function if each x-value maps to exactly one y-value

Theorems

Definition of a function

Suitable Grade Level

Grade 8-9