Algebra worksheet featuring six graphing problems with linear and absolute value functions on coordinate grids.

1. f(x) = x
- Graph: Straight line through origin with slope 1.
- Domain: All real numbers (−∞, ∞)
- Range: All real numbers (−∞, ∞)

2. f(x) = 3x + 4
- Graph: Straight line with slope 3 and y-intercept 4.
- Domain: All real numbers (−∞, ∞)
- Range: All real numbers (−∞, ∞)

3. f(x) = 1/x − 1
- Graph: Hyperbola shifted down by 1 unit; vertical asymptote at x=0, horizontal asymptote at y=−1.
- Domain: All real numbers except x=0 (−∞, 0) ∪ (0, ∞)
- Range: All real numbers except y=−1 (−∞, −1) ∪ (−1, ∞)

4. f(x) = |x|
- Graph: V-shape with vertex at origin.
- Domain: All real numbers (−∞, ∞)
- Range: [0, ∞)

5. f(x) = |x − 3| − 3
- Graph: V-shape shifted right 3 units and down 3 units; vertex at (3, −3).
- Domain: All real numbers (−∞, ∞)
- Range: [−3, ∞)

6. f(x) = 4|x − 6| + 1
- Graph: V-shape shifted right 6 units, up 1 unit, and vertically stretched by factor of 4; vertex at (6, 1).
- Domain: All real numbers (−∞, ∞)
- Range: [1, ∞)