
Unless otherwise stated:
Domain: x > 0 or [0,∞)
Range: y > 0 or [0,∞)

Features (of parent function):
• increasing function [0,∞)
• positive function (0,∞)
• no absolute max (graph → ∞)
• absolute minimum 0
• no relative max/min
• end behavior
f (x)
→ +∞, as x → +∞
f (x)
→ 0, as x → 0


Average rate of change: (slope) NOT constant.
xintercept:
intersects xaxis at
(0, 0)
unless domain is altered
yintercept:
intersects yaxis at
(0, 0)
unless domain is altered
Note:
This function is the positive square root only.


Table:
Y1:
Remember: The square root of a negative number is imaginary. 
Connection to y = x²:
[Reflect y = x² over the line y = x.]
If we solve y = x² for x:, we get the inverse.
We can see that the square root function is "part" of the inverse of y = x².
Keep in mind that the square root function only utilizes the positive square root. If both positive and negative square root values were used, it would not be a function. 






Square Root Function  Transformation Examples:
Unless otherwise stated:
Domain: All Reals or (∞,∞)
Range: All Reals or (∞,∞)

Features (of parent function):
• increasing (∞,∞)
• positive (0,∞)
• negative (∞,0)
• no absolute max (graph → ∞)
• no absolute min (graph→ ∞)
• no relative max or min
• end behavior
f (x)
→ +∞, as x → +∞
f (x)
→ ∞, as x → ∞
• symmetric about origin


Average rate of change: (slope) NOT constant.
xintercept:
intersects xaxis at
(0, 0)
unless domain is altered
yintercept:
intersects yaxis at
(0, 0)
unless domain is altered
Note:
Unlike the square root function, the cube root function can process negative values.

Cube Root Function  Transformation Examples:
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