Math Problem Statement
Consider the table of values and determine which of the following statements is true regarding the relationship between x and y, particularly in terms of whether the relationship is a function.
Solution
The table of values in the image provides pairs of and values. To determine if this relationship is a function, we must apply the definition of a function: A relation is a function if and only if each input is mapped to exactly one output .
Let’s examine the table:
\hline x & y \\ \hline -7 & 10 \\ -4 & 5 \\ -3 & 2 \\ 0 & 1 \\ 1 & 2 \\ -4 & 6 \\ -2 & 8 \\ \hline \end{array}$$ Notice that the input $$x = -4$$ maps to two different $$y$$-values (5 and 6). This violates the definition of a function, where an input must have only one corresponding output. Therefore, the correct statement is: - "This relationship is **NOT** a function from $$x$$ to $$y$$ because $$x = -4$$ gets mapped to two different $$y$$-values." ### Would you like more details on functions or clarifications? Here are some related questions: 1. What are the conditions that must be met for a relationship to be a function? 2. How do you determine if a set of points defines a function? 3. Can a function map different inputs to the same output? 4. What is the vertical line test in the context of functions? 5. How do one-to-one functions differ from regular functions? **Tip**: In a table, check if any input repeats with different outputs to easily spot whether the relation is a function.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Functions
Relations
Mapping
Formulas
-
Theorems
Definition of a Function
Suitable Grade Level
Grades 8-10