Explanation:
Function 1: y = √(x + 2)
Domain: x ≥ -2
Range: y ≥ 0
x-intercept: (-2, 0)
y-intercept: (0, √2)
Transformations: This is the parent function shifted 2 units to the left.
Three points: (-2, 0), (0, √2), (6, 2)
Function 2: y = -√(x - 3)
Domain: x ≥ 3
Range: y ≤ 0
x-intercept: (3, 0)
y-intercept: (0, -√3)
Transformations: This is the parent function reflected over the x-axis and shifted 3 units to the right.
Three points: (3, 0), (4, -1), (5, -√2)
Function 3: y = √(4 - x^2)
Domain: -2 ≤ x ≤ 2
Range: 0 ≤ y ≤ 2
x-intercepts: (-2, 0) and (2, 0)
y-intercept: (0, 2)
Transformations: This is the top half of a circle with radius 2, centered at the origin.
Three points: (-2, 0), (0, 2), (2, 0)
I hope that helps!