Vocabulary
Domain
All of the x-values which make the function true
y = sqrt (x + 3)
Translation - 3 units to the left
Domain - x >= -3
Range - y >= 0
y = 1/2(sqrt x - 3) + 2
Vertical compression
Translation: 3 units to the right
Translation: 2 units up
Domain: x >= 3
Range: y >= 2
All the y-values that make a function true
y = -(sqrt x) + 5
Reflection over the x-axis
Translation: 5 units up
Domain: x >= 0
Range: y <= 5
y = -(sqrt x + 5.6)
Reflection over x-axis
Translation: 5.6 units to the left
Domain: x >= -5.6
Range: y <= 0
Vertical stretch/compression
Making the graph narrower/wider without changing the domain and range
y = -1/2(sqrt x)
Reflection over x-axis
Vertical compression
Domain: x >= 0
Range: y <= 0
y = -6(sqrt x) + 5
Reflection over x-axis
Vertical stretch
Translation: 5 units up
Domain: x >= 0
Range: y <= 5
Reflection
Flipping the graph over the x- or y- axis
y = -(sqrt x + 5)
Reflection over x-axis
Translation: 5 units to the left
Domain: x >= -5
Range: y <= 0
Translation: 4 units down
Domain: x >= 0
Range: y >= -4
y = (sqrt x) - 4
Radicand
The expression underneath the square root symbol
y = sqrt (x) - 1.5
Translation: 1.5 units down
Domain: x >= 0
Range: y >= 1.5
Translation: 5 units to the left
Reflection over the x-axis
Domain: x >= -5
Range: y <= 0
y = -(sqrt x + 5)