sqrootfeatures2
SRmath1
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.
positiveSR

Table: Y1: tableeq
SRgraph3Remember: 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:invereex, 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.
sr2

Square Root Function - Transformation Examples:

SRgraph6
Translations
SRgraph5
Reflection
SRgraph7
Vertical Stretch/Shrink

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crfeatures
CRgraph2Unless 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: CRwq
CRgraph1
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:
inversec, 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:
CR8
CRgraph3

Cube Root Function - Transformation Examples:
CRgraph5
Translations
CRgraph4
Reflection
CRgraph66
Vertical Stretch/Shrink

 

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