1. Domain: x = All Real Numbers (-∞, ∞)
         Range: y = All Real Numbers (-∞, 7]
         Graph: see attachment 1
1. Step-by-step explanation:
NOTE: When graphing a piecewise function, think of it as sharing the graph with 2 lines. The length of the lines are restricted by the inequality provided.
Graph y = x  → the line ENDS when x = -3 with a closed dot
Graph y = -2x+1 → the line STARTS when x = -3 with an open dot
There are no restrictions on x so the Domain is "All Real Numbers"
In interval notation, it is written as: (-∞, ∞)
Since both slopes are negative, there is a maximum value for y so the Range is: y < 7
In interval notation, it is written as: (-∞, 7)
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2. Domain: x = All Real Numbers (-∞, ∞)
         Range: y = All Real Numbers (-∞, ∞)
         Graph: see attachment 2
2. Step-by-step explanation:
Graph  → the line ENDS when x = 2 with an open dot
Graph y = x+2 → the line STARTS when x = 2 with a closed dot
There are no restrictions on x so the Domain is "All Real Numbers"
In interval notation, it is written as: (-∞, ∞)
Since there is one slope positive and the other slope negative, there are no restrictions on y so the Range is: "All Real Numbers"
In interval notation, it is written as: (-∞, ∞)
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3. Domain: x = All Real Numbers (-∞, ∞)
         Range: y = All Real Numbers (-∞, 1/3]
         Graph: see attachment 3
3. Step-by-step explanation:
Graph  → the line STARTS when x = -1 with an open dot
Graph y = x+2 → the line ENDS when x = -1 with a closed dot
There are no restrictions on x so the Domain is "All Real Numbers"
In interval notation, it is written as: (-∞, ∞)
Since both slopes are negative, there is a maximum value for y so the Range is: y ≤ 1/3
In interval notation, it is written as: (-∞, 1/3]