Question

identify the domain & range for each graph below:
3
domain:
range:
4
domain:
range:

1. domain: inequalities
2. domain: interval notation
3. range: inequalities
4. range: interval notation
5. domain: inequalities
6. domain: interval notation
7. range: inequalities
8. range: interval notation

Explanation:

Step1: Analyze Graph 3 (V - shaped graph)

Domain (x - values):

The graph extends horizontally from \( x=-3 \) to \( x = 3 \) (inclusive, as the vertices are at \( x=-3 \) and \( x = 3 \)). So in inequalities: \( -3\leq x\leq3 \); in interval notation: \( [-3,3] \).

Range (y - values):

The graph extends vertically from \( y = 0 \) (the vertex at the bottom) up to \( y=4 \) (the top vertices). So in inequalities: \( 0\leq y\leq4 \); in interval notation: \( [0,4] \).

Step2: Analyze Graph 4 (Rectangular graph)

Domain (x - values):

The rectangle spans from \( x=-2 \) to \( x = 2 \) (inclusive, since the sides are at \( x=-2 \) and \( x = 2 \)). In inequalities: \( -2\leq x\leq2 \); in interval notation: \( [-2,2] \).

Range (y - values):

The rectangle spans from \( y=-3 \) to \( y = 3 \) (inclusive, as the top and bottom sides are at \( y = 3 \) and \( y=-3 \)). In inequalities: \( -3\leq y\leq3 \); in interval notation: \( [-3,3] \).

Answer:

1. Domain: Inequalities: \( -3\leq x\leq3 \); Interval Notation: \( [-3,3] \)
2. Range: Inequalities: \( 0\leq y\leq4 \); Interval Notation: \( [0,4] \)
3. Domain: Inequalities: \( -2\leq x\leq2 \); Interval Notation: \( [-2,2] \)
4. Range: Inequalities: \( -3\leq y\leq3 \); Interval Notation: \( [-3,3] \)