Question

domain & range: continuous
1.
domain
range
2.
domain:
range

1. inequalities

domain:
≤ x ≤
range:
≤ y ≤

1. domain:

< x ≤
range:
≤ y <

Explanation:

Step1: Analyze Graph 1 (Problem 1)

• Domain: The left endpoint of the line segment is at \( x = -4 \) (filled dot) and the right endpoint is at \( x = 1 \) (filled dot). So domain is \( -4 \leq x \leq 1 \).
• Range: The bottom endpoint is at \( y = -3 \) (filled dot) and the top endpoint is at \( y = 4 \) (filled dot). So range is \( -3 \leq y \leq 4 \).

Step2: Analyze Graph 2 (Problem 2)

• Domain: The left endpoint is an open dot at \( x = -4 \) (so \( x > -4 \)) and the right endpoint is a filled dot at \( x = 4 \) (so \( x \leq 4 \)). Thus domain is \( -4 < x \leq 4 \).
• Range: The bottom endpoint is a filled dot at \( y = -4 \) and the top endpoint is an open dot at \( y = 4 \) (so \( y < 4 \)). Thus range is \( -4 \leq y < 4 \).

Answer:

1. Domain: \( \boldsymbol{-4 \leq x \leq 1} \), Range: \( \boldsymbol{-3 \leq y \leq 4} \)
2. Domain: \( \boldsymbol{-4 < x \leq 4} \), Range: \( \boldsymbol{-4 \leq y < 4} \)