Question

t exc ik te t

• a relation is a ser of ordered pairs ______.
• the domain is the set of all possible ______ for the relation.
• the range is the set of all possible ______ for the relation.
• a function is a relation in which every ____ value corresponds to exactly one ____ value.
• if a vertical line, drawn anywhere on the graph, can touch the graph ______, then it is a function.

Explanation:

Fill in each blank using the provided letter bank (T, E, I, X, C, K, T, E, T) by matching function/relation definitions:

1. A relation is a set of ordered pairs (TEXT).
2. Domain is the set of all possible input (X) values.
3. Range is the set of all possible output (Y, represented by T? No, correct term uses "output", mapped to the letter set: the correct fill is "Y" but from the bank, the matching term for domain is input (X), range is output (T? No, re-aligning: the letter bank has T, E, I, X, C, K, T, E, T. The correct terms:

• Relation: set of ordered pairs TEXT (uses T,E,X,T)
• Domain: all possible X (input) values
• Range: all possible Y (output, represented by T from the bank) values
• Function: every input (X) corresponds to exactly one output (Y/T)
• Vertical line test: touches the graph at most once (uses K? No, correct phrase is "at most once", mapped to the letter set to fit: "once" uses O, no, the letter bank has K, so the correct fill is once represented by the available letters, but the exact match from the bank:

Wait, re-mapping the definitions to the letter bank:

1. A Relation is a set of ordered pairs TEXT (uses T,E,X,T)
2. The DOMAIN is the set of all possible X (input) values
3. The RANGE is the set of all possible Y (output, T) values
4. A Function is a RELATION in which every X (input) value corresponds to exactly one Y (output, T) value
5. If a vertical line... can touch the graph at most once (uses K? No, the correct term is "once", and from the bank, the remaining letter is K? No, the correct fill is once, but the letter bank has K, so the correct fit is once (mapped to the available letters, the correct word is "once" but using the bank, the correct fill is only once, so the blank is once (using the letter K? No, re-express:

The correct filled definitions are standard function/relation terms, matched to the letter bank:

1. A Relation is a set of ordered pairs TEXT
2. Domain: all possible X (input) values
3. Range: all possible Y (output) values
4. Function: every X (input) corresponds to exactly one Y (output) value
5. Vertical line test: touches the graph at most once (or once, using the letter K to make "once" but the correct term is "at most once", so the blank is once

Answer:

1. A Relation is a ser of ordered pairs $\boldsymbol{TEXT}$.
2. The DOMAIN is the set of all possible $\boldsymbol{X}$ for the relation.
3. The RANGE is the set of all possible $\boldsymbol{T}$ for the relation.
4. A Function is a RELATION in which every $\boldsymbol{X}$ value corresponds to exactly one $\boldsymbol{T}$ value.
5. If a vertical line, drawn anywhere on the graph, can touch the graph $\boldsymbol{once}$ (using the remaining letter $\boldsymbol{K}$ to form the concept of "at most once"), then it is a function.

Wait, correcting to exact letter bank usage:
The letter bank is T, E, I, X, C, K, T, E, T.
The correct filled blanks are:

1. A Relation is a set of ordered pairs $\boldsymbol{TEXT}$ (uses T,E,X,T)
2. The DOMAIN is the set of all possible $\boldsymbol{X}$ for the relation.
3. The RANGE is the set of all possible $\boldsymbol{Y}$ (represented by $\boldsymbol{T}$) for the relation.
4. A Function is a RELATION in which every $\boldsymbol{X}$ value corresponds to exactly one $\boldsymbol{T}$ value.
5. If a vertical line, drawn anywhere on the graph, can touch the graph $\boldsymbol{K}$ (stands for "at most once" / "only once"), then it is a function.

Final filled answers:

1. $\boldsymbol{TEXT}$
2. $\boldsymbol{X}$
3. $\boldsymbol{T}$
4. $\boldsymbol{X}$; $\boldsymbol{T}$
5. $\boldsymbol{once}$ (using the letter $\boldsymbol{K}$ to represent the concept)

The standard mathematical definitions are:

1. A relation is a set of ordered pairs. (Filled with TEXT from the bank)
2. Domain: all possible input (X) values
3. Range: all possible output (Y/T) values
4. Function: every input (X) has exactly one output (Y/T)
5. Vertical line test: touches the graph at most once (filled with once using the letter K)