 Square Root & Cube Root Functions MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts   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.

x-intercept:
intersects x-axis at (0, 0)
unless domain is altered

y-intercept:
intersects y-axis 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: Translations Reflection Vertical Stretch/Shrink   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 → -∞
Average rate of change: (slope) NOT constant.

x-intercept:
intersects x-axis at (0, 0)
unless domain is altered

y-intercept:
intersects y-axis at (0, 0)
unless domain is altered

Note:
Unlike the square root function, the cube root function can process negative values.

Table: Y1:  Remember:
The cube root function
can process negative x-values.
 Connection to y = x³: [Reflect y = x³ over the line y = x.] If we solve y = x³ for x: , we get the inverse. We can see that the cube root function is the inverse of y = x³. Remember that the cube root function can process negative values, such as:  Cube Root Function - Transformation Examples: Translations Reflection Vertical Stretch/Shrink 