Let's solve and complete the worksheet titled
"Relations & Functions Notes" step by step. The goal is to fill in the blanks based on mathematical definitions and examples provided.
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🔹 Definitions at the Top
relation - A
relationship between sets of values. The two types of values are called
inputs and
outputs.
>
✔ Explanation: A *relation* is a set of ordered pairs showing how inputs (x-values) relate to outputs (y-values). These are also known as domain and range.
function - A special type of
relation where each input has only
one output.
>
✔ Explanation: A *function* is a relation where every input (x-value) maps to exactly one output (y-value). This is the "vertical line test" principle.
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🔹 Ways to Represent Relations
#### 1.
ORDERED PAIRS
-
Definition: The
x coordinate and
y coordinate of a point.
-
✔ Explanation: In an ordered pair $(x, y)$, $x$ is the horizontal coordinate (input), and $y$ is the vertical coordinate (output).
#### 2.
X-Y TABLE
-
Definition: A table that shows inputs and outputs in terms of
x and
y.
-
✔ Explanation: The left column represents input values (x), and the right column represents output values (y). It’s a structured way to list data points.
#### 3.
MAPPING DIAGRAM
-
Definition: A type of diagram that shows the relationship between each
input and
output by using arrows.
-
✔ Explanation: The mapping diagram visually connects each element from the domain (input) to its corresponding element in the range (output). Each arrow shows a pairing.
#### 4.
GRAPH
-
Definition: A visual display of
points.
-
✔ Explanation: A graph plots ordered pairs $(x, y)$ on the coordinate plane. The collection of these plotted points represents the relation or function.
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✔ Final Completed Worksheet:
```
relation - A relationship between sets of values. The two types of values are called inputs and outputs.
function - A special type of relation where each input has only one output.
WAYS TO REPRESENT RELATIONS
| WORD | DEFINITION | EXAMPLE |
|----------------|---------------------------------------------------------------------------|----------------------------------|
| ORDERED PAIRS | The x coordinate and y coordinate of a point. | (x,y) <br> (1,3), (2,1), (3,4), (5,2) |
| X-Y TABLE | A table that shows inputs and outputs in terms of x and y. | x | y <br> 1 | 3 <br> 2 | 1 <br> 3 | 4 <br> 5 | 2 |
| MAPPING DIAGRAM| A type of diagram that shows the relationship between each input and output by using arrows. | input → output <br> 1→1, 2→2, 3→3, 5→4 |
| GRAPH | A visual display of points. | Plot of points on coordinate plane |
```
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📌 Summary:
This worksheet teaches students how to understand and represent
relations and
functions in four different ways:
1.
Ordered Pairs – List of $(x, y)$
2.
X-Y Table – Tabular form
3.
Mapping Diagram – Arrows from inputs to outputs
4.
Graph – Plotted points on a coordinate plane
A
function is a special case of a relation where
each input has exactly one output, which can be checked using the
vertical line test on a graph.
✔ All blanks have been filled correctly with standard math terminology.
Parent Tip: Review the logic above to help your child master the concept of functions and relations worksheet.
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