Answer: see below
Step-by-step explanation:
Domain is all of the x-values. Notice that every x-value is included except the points between x = 0 and x = 1.
D: x = (-∞, 0] ∪ (1, ∞)
Range is all of the y-values. Notice that every y-value is included except the points between y = 3 and y = 6.
R: y = (-∞, 3] ∪ [6, ∞)
x-intercepts are where the lines cross the x-axis (when y = 0).
x = -3, x = 3 This can also be written as coordinates (-3, 0) & (3, 0)
y-intercepts are where the lines cross the y-axis (when x = 0).
y = 3 This can also be written as coordinate (0, 3)
Maximum is the largest y-value.
y = ∞
Minimum is the smallest y-value:
y = -∞
Increasing is the x-values when the line is going UPWARD from left to right (positive slope). This occurs for the x + 3 (when x ≤ 0) and 2x (when x > 3)
Increasing: x = (-∞, 0] ∪ (3, ∞)
Decreasing is the x-values when the line is going DOWNWARD from left to right (negative slope). This occurs for the 3 - x (when 1 < x ≤ 3)
Decreasing: x = (1, 3]
Positive is the x-values when the y-values are positive (above the x-axis).
This occurs between x = 3 and x = 0 and when x is greater than 1 (except at 3).
Positive: (-3, 0] ∪ (1, 3) ∪ (3, ∞)
Negative is the x-values when the y-values are negative (below the x-axis).
This occurs when x is less than -3.
Positive: (-∞, -3)
End behavior: as x moves to the right (positive infinity), y goes up
as x → ∞, y → ∞
as x moves to the left (negative infinity), y goes down
as x → -∞, y → -∞
f(1) means find the y-value when x = 1. Since there is no x-value at 1, there is no y-value.
f(1) = Does Not Exist
