Question

domain and range matching
match the domain and range cards with the graphs below.
you must use 2 colors to draw the domain and range lines of each function.

(graphs and domain-range cards as shown, with some filled or handwritten details like:
domain: -2 ≤ x ≤ 5; domain: -3 ≤ x ≤ 6; domain: -4 ≤ x ≤ blank; domain: -3 ≤ x ≤ 2; range: 1 ≤ f(x) ≤ 5; range: 1 ≤ h(x) ≤ 6; range: -3 ≤ f(x) ≤ 5; range: -5 ≤ f(x) ≤ 0;
domain: 0 ≤ x ≤ 4.5; range: 0 ≤ f(x) ≤ 3; and other handwritten domain/range entries on cards, along with more graphs below)

Explanation:

To solve the domain and range matching for the given graphs, we analyze each graph's horizontal (domain) and vertical (range) extent:

1. First Graph (Top - Left)

• Domain: The graph spans \( x \)-values from \( -2 \) to \( 5 \), so \( -2 \leq x \leq 5 \).
• Range: The graph spans \( y \)-values from \( 1 \) to \( 5 \), so \( 1 \leq f(x) \leq 5 \).

2. Second Graph (Top - Middle - Left)

• Domain: The graph spans \( x \)-values from \( -3 \) to \( 6 \), so \( -3 \leq x \leq 6 \).
• Range: The graph spans \( y \)-values from \( 1 \) to \( 6 \), so \( 1 \leq h(x) \leq 6 \).

3. Third Graph (Top - Middle - Right)

• Domain: The graph spans \( x \)-values from \( -4 \) to \( 4 \), so \( -4 \leq x \leq 4 \).
• Range: The graph spans \( y \)-values from \( -3 \) to \( 5 \), so \( -3 \leq f(x) \leq 5 \).

4. Fourth Graph (Top - Right)

• Domain: The graph spans \( x \)-values from \( -3 \) to \( 2 \), so \( -3 \leq x \leq 2 \).
• Range: The graph spans \( y \)-values from \( -5 \) to \( 0 \), so \( -5 \leq f(x) \leq 0 \).

5. Fifth Graph (Middle - Left)

• Domain: The graph spans \( x \)-values from \( 0 \) to \( 4.5 \), so \( 0 \leq x \leq 4.5 \).
• Range: The graph spans \( y \)-values from \( 0 \) to \( 3 \), so \( 0 \leq f(x) \leq 3 \).

6. Sixth Graph (Middle - Middle - Left)

• Domain: The graph spans \( x \)-values from \( 0 \) to \( 9 \) (or similar, based on grid), so \( 0 \leq x \leq 9 \).
• Range: The graph spans \( y \)-values from \( 0 \) to \( 4 \), so \( 0 \leq f(x) \leq 4 \).

7. Seventh Graph (Middle - Middle - Right)

• Domain: The graph spans \( x \)-values from \( 0 \) to \( 360 \) (or similar, based on grid), so \( 0 \leq x \leq 360 \).
• Range: The graph spans \( y \)-values from \( -1 \) to \( 1 \), so \( -1 \leq f(x) \leq 1 \).

8. Eighth Graph (Middle - Right)

• Domain: The graph spans \( x \)-values from \( 0 \) to \( 9 \) (or similar, based on grid), so \( 0 \leq x \leq 9 \).
• Range: The graph spans \( y \)-values from \( 0 \) to \( 4 \), so \( 0 \leq f(x) \leq 4 \) (consistent with the sixth graph’s range pattern).

Final Matches (Example for Key Cards):

Graph Position	Domain	Range
Top - Middle - Left	\( -3 \leq x \leq 6 \)	\( 1 \leq h(x) \leq 6 \)
Top - Middle - Right	\( -4 \leq x \leq 4 \)	\( -3 \leq f(x) \leq 5 \)
Top - Right	\( -3 \leq x \leq 2 \)	\( -5 \leq f(x) \leq 0 \)
Middle - Left	\( 0 \leq x \leq 4.5 \)	\( 0 \leq f(x) \leq 3 \)

To complete the task, use two colors (e.g., blue for domain, red for range) to draw horizontal/vertical lines marking the domain (x - axis extent) and range (y - axis extent) for each graph.

Answer:

To solve the domain and range matching for the given graphs, we analyze each graph's horizontal (domain) and vertical (range) extent:

1. First Graph (Top - Left)

• Domain: The graph spans \( x \)-values from \( -2 \) to \( 5 \), so \( -2 \leq x \leq 5 \).
• Range: The graph spans \( y \)-values from \( 1 \) to \( 5 \), so \( 1 \leq f(x) \leq 5 \).

2. Second Graph (Top - Middle - Left)

• Domain: The graph spans \( x \)-values from \( -3 \) to \( 6 \), so \( -3 \leq x \leq 6 \).
• Range: The graph spans \( y \)-values from \( 1 \) to \( 6 \), so \( 1 \leq h(x) \leq 6 \).

3. Third Graph (Top - Middle - Right)

• Domain: The graph spans \( x \)-values from \( -4 \) to \( 4 \), so \( -4 \leq x \leq 4 \).
• Range: The graph spans \( y \)-values from \( -3 \) to \( 5 \), so \( -3 \leq f(x) \leq 5 \).

4. Fourth Graph (Top - Right)

• Domain: The graph spans \( x \)-values from \( -3 \) to \( 2 \), so \( -3 \leq x \leq 2 \).
• Range: The graph spans \( y \)-values from \( -5 \) to \( 0 \), so \( -5 \leq f(x) \leq 0 \).

5. Fifth Graph (Middle - Left)

• Domain: The graph spans \( x \)-values from \( 0 \) to \( 4.5 \), so \( 0 \leq x \leq 4.5 \).
• Range: The graph spans \( y \)-values from \( 0 \) to \( 3 \), so \( 0 \leq f(x) \leq 3 \).

6. Sixth Graph (Middle - Middle - Left)

• Domain: The graph spans \( x \)-values from \( 0 \) to \( 9 \) (or similar, based on grid), so \( 0 \leq x \leq 9 \).
• Range: The graph spans \( y \)-values from \( 0 \) to \( 4 \), so \( 0 \leq f(x) \leq 4 \).

7. Seventh Graph (Middle - Middle - Right)

• Domain: The graph spans \( x \)-values from \( 0 \) to \( 360 \) (or similar, based on grid), so \( 0 \leq x \leq 360 \).
• Range: The graph spans \( y \)-values from \( -1 \) to \( 1 \), so \( -1 \leq f(x) \leq 1 \).

8. Eighth Graph (Middle - Right)

• Domain: The graph spans \( x \)-values from \( 0 \) to \( 9 \) (or similar, based on grid), so \( 0 \leq x \leq 9 \).
• Range: The graph spans \( y \)-values from \( 0 \) to \( 4 \), so \( 0 \leq f(x) \leq 4 \) (consistent with the sixth graph’s range pattern).

Final Matches (Example for Key Cards):

Graph Position	Domain	Range
Top - Middle - Left	\( -3 \leq x \leq 6 \)	\( 1 \leq h(x) \leq 6 \)
Top - Middle - Right	\( -4 \leq x \leq 4 \)	\( -3 \leq f(x) \leq 5 \)
Top - Right	\( -3 \leq x \leq 2 \)	\( -5 \leq f(x) \leq 0 \)
Middle - Left	\( 0 \leq x \leq 4.5 \)	\( 0 \leq f(x) \leq 3 \)

To complete the task, use two colors (e.g., blue for domain, red for range) to draw horizontal/vertical lines marking the domain (x - axis extent) and range (y - axis extent) for each graph.