Question

find the domain and range for each graph. 1) domain: __ range: 2) domain: range: 3) domain: range: 4) domain: range: 5) domain: range: 6) domain: range: 7) domain: range: 8) domain: range: 9) domain: range: __

Answer:

1. For the first graph:

• Explanation:
• Step 1: Identify domain
• The left - most \(x\) value is \(- 4\) (open - circle) and the right - most \(x\) value is \(0\) (closed - circle). So the domain is all \(x\) values from \(-4\) to \(0\), written as \(-4\lt x\leqslant0\).
• Step 2: Identify range
• The lowest \(y\) value is \(-4\) (closed - circle) and the highest \(y\) value is \(4\) (open - circle). So the range is \(-4\leqslant y\lt4\).
• Answer:
• Domain: \(-4\lt x\leqslant0\)
• Range: \(-4\leqslant y\lt4\)

1. For the second graph:

• Explanation:
• Step 1: Identify domain
• The left - most \(x\) value is \(-3\) (closed - circle) and the right - most \(x\) value is \(3\) (open - circle). So the domain is \(-3\leqslant x\lt3\).
• Step 2: Identify range
• The lowest \(y\) value is \(-2\) (closed - circle) and the highest \(y\) value is \(3\) (closed - circle). So the range is \(-2\leqslant y\leqslant3\).
• Answer:
• Domain: \(-3\leqslant x\lt3\)
• Range: \(-2\leqslant y\leqslant3\)

1. For the third graph:

• Explanation:
• Step 1: Identify domain
• The left - most \(x\) value is \(-4\) (closed - circle) and the right - most \(x\) value is \(4\) (closed - circle). So the domain is \(-4\leqslant x\leqslant4\).
• Step 2: Identify range
• The lowest \(y\) value is \(-3\) (closed - circle) and the highest \(y\) value is \(2\) (closed - circle). So the range is \(-3\leqslant y\leqslant2\).
• Answer:
• Domain: \(-4\leqslant x\leqslant4\)
• Range: \(-3\leqslant y\leqslant2\)

1. For the fourth graph:

• Explanation:
• Step 1: Identify domain
• The left - most \(x\) value is \(-4\) (closed - circle) and the right - most \(x\) value is \(-1\) (open - circle). So the domain is \(-4\leqslant x\lt - 1\).
• Step 2: Identify range
• The lowest \(y\) value is \(1\) (closed - circle) and the highest \(y\) value is \(5\) (closed - circle). So the range is \(1\leqslant y\leqslant5\).
• Answer:
• Domain: \(-4\leqslant x\lt - 1\)
• Range: \(1\leqslant y\leqslant5\)

1. For the fifth graph:

• Explanation:
• Step 1: Identify domain
• The left - most \(x\) value is \(-4\) (closed - circle) and the right - most \(x\) value is \(4\) (closed - circle). So the domain is \(-4\leqslant x\leqslant4\).
• Step 2: Identify range
• The lowest \(y\) value is \(-5\) (closed - circle) and the highest \(y\) value is \(1\) (closed - circle). So the range is \(-5\leqslant y\leqslant1\).
• Answer:
• Domain: \(-4\leqslant x\leqslant4\)
• Range: \(-5\leqslant y\leqslant1\)

1. For the sixth graph:

• Explanation:
• Step 1: Identify domain
• The left - most \(x\) value is \(-4\) (open - circle) and the right - most \(x\) value is \(4\) (open - circle). So the domain is \(-4\lt x\lt4\).
• Step 2: Identify range
• The lowest \(y\) value is \(0\) (closed - circle) and there is no upper - bound in the visible part of the graph. So the range is \(y\geqslant0\).
• Answer:
• Domain: \(-4\lt x\lt4\)
• Range: \(y\geqslant0\)

1. For the seventh graph:

• Explanation:
• Step 1: Identify domain
• The left - most \(x\) value is \(-4\) (closed - circle) and the right - most \(x\) value is \(4\) (open - circle). So the domain is \(-4\leqslant x\lt4\).
• Step 2: Identify range
• The lowest \(y\) value is \(-3\) (closed - circle) and the highest \(y\) value is \(4\) (closed - circle). So the range is \(-3\leqslant y\leqslant4\).
• Answer:
• Domain: \(-4\leqslant x\lt4\)
• Range: \(-3\leqslant y\leqslant4\)

1. For the eighth graph:

• Explanation:
• Step 1: Identify domain
• The left - most \(x\) value is \(-3\) (closed - circle) and the right - most \(x\) value is \(3\) (open - circle). So the domain is \(-3\leqslant x\lt3\).
• Step 2: Identify range
• The lowest \(y\) value is \(-5\) (closed - circle) and the highest \(y\) value is \(3\) (closed - circle). So the range is \(-5\leqslant y\leqslant3\).
• Answer:
• Domain: \(-3\leqslant x\lt3\)
• Range: \(-5\leqslant y\leqslant3\)

1. For the ninth graph:

• Explanation:
• Step 1: Identify domain
• The left - most \(x\) value is \(-3\) (closed - circle) and the right - most \(x\) value is \(3\) (closed - circle). So the domain is \(-3\leqslant x\leqslant3\).
• Step 2: Identify range
• The lowest \(y\) value is \(0\) (closed - circle) and the highest \(y\) value is \(3\) (closed - circle). So the range is \(0\leqslant y\leqslant3\).
• Answer:
• Domain: \(-3\leqslant x\leqslant3\)
• Range: \(0\leqslant y\leqslant3\)