Let’s go through the worksheet step by step to fill in all the blanks correctly.
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Top Section: Definitions
1.
relation – A *relationship* between sets of values. The two types of values are called *input* and *output*.
→ This is standard math terminology. In relations, we pair inputs with outputs.
2.
function – A special type of *relation* where each input has only *one* output.
→ That’s the key difference: functions can’t have one input giving multiple outputs.
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Ways to Represent Relations Table
We’ll go row by row.
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Row 1: ORDERED PAIRS
Definition: The ___ coordinate and ___ coordinate of a point.
→ Ordered pairs are written as (x, y), so it’s the *first* coordinate and *second* coordinate — or more precisely, *x* and *y*. But since the example shows (x,y), and the blank says “coordinate”, we should say:
first and
second
OR
x and
y
But looking at context — later rows use x and y explicitly — here it’s better to be general. Since it says “the ___ coordinate”, likely expecting “x” and “y”.
Actually, let’s check common phrasing: “The x-coordinate and y-coordinate of a point.” Yes, that’s standard.
So:
x and
y
Example given: (1,3), etc. — matches.
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Row 2: X-Y TABLE
Definition: A table that shows inputs and outputs in terms of ___ and ___.
→ Looking at the example table, columns are labeled ‘x’ and ‘y’. So again,
x and
y.
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Row 3: MAPPING DIAGRAM
Definition: A type of diagram that shows the relationship between each ________ and ________ by using arrows.
→ From the image: left oval is “input”, right is “output”, arrows connect them.
So:
input and
output
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Row 4: GRAPH
Definition: A visual display of ________.
→ A graph visually displays the relation — specifically, the ordered pairs plotted on axes.
Common phrase: “A visual display of data” or “of the relation” or “of points”.
Looking at the example: it’s plotting points from the relation. So best answer:
points or
ordered pairs
But simplest and most accurate for this level:
points
Alternatively, sometimes they say “a visual display of the relationship” — but the blank is short, and “points” fits well.
Wait — let’s think: what does a graph show? It shows the location of points representing the relation. So “points” is good.
Some might say “data”, but “points” is more precise here.
Final decision:
points
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Now double-check everything:
- relation → relationship; input, output
✔
- function → relation; one
✔
- ordered pairs → x, y
✔
- x-y table → x, y
✔
- mapping diagram → input, output
✔
- graph → points
✔
All make sense and match standard middle/high school math definitions.
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Final Answer:
relation - A
relationship between sets of values. The two types of values are called
input and
output.
function - A special type of
relation where each input has only
one output.
ORDERED PAIRS: The
x coordinate and
y coordinate of a point.
X-Y TABLE: ... in terms of
x and
y.
MAPPING DIAGRAM: ... between each
input and
output ...
GRAPH: A visual display of
points.
Parent Tip: Review the logic above to help your child master the concept of worksheet algebraic relations.
