Aim#56GraphingCubeRootSquareRootCubicFunctions.notebook
February 25, 2015
Unit 9 - Aim #56
Graphing Square Root,
Cubic, & Cube Root Functions
Objective
You will be able to:
• Compare the basic Quadratic Function y = x2, to the Square Root Function.
• Compare the basic Cubic Function y = x3, to the Cube Root Function.
• Sketch graphs of Square Root and Cube Root Functions,
given any constraints on the domain and range.
********************************************* *********************************************
DO NOW:
Evaluate x2 when x = 7.
Evaluate
_____
when x = 81. _____
Evaluate x3 when x = 5. _____
Evaluate
when x = 27. _____
1
Aim#56GraphingCubeRootSquareRootCubicFunctions.notebook
February 25, 2015
Let's Explore Functions with our Calculator! Use your graphing calculator to create a data table for the functions for the x­values given. Round decimal answers to the nearest hundredth. 4
2
0
­2
­4
Domain of y = x2 is:
________________
is: Domain of ________________
Range of y = x2 is:
________________
is: Range of ________________
DISCUSSION: ­ What do you notice about the values of both ranges (y­values)? All y­values are 0 or positive #'s except for those produced by negative x­values.
­ Why are the y­values for y = x2 all positive?
Whenever you square a # whether positive or negative,
the result will be positive.
­ Why do the negative x­values produce an error for ?
No real # when squared produces a negative result. The square root of a negative # is an imaginary number.
2
Aim#56GraphingCubeRootSquareRootCubicFunctions.notebook
February 25, 2015
Let's loo k at graphs of these functions!
Create the graphs of y = x2 and on the same set of axes. Steps to Calculator: Go to Y =
Type in functions into Y1 and Y2. Make Y2 a darker line. Press GRAPH . Press 2ND then TABLE
Plot points from table. (choose points that aren't decimals.) ­ What additional observations can we make when comparing the
GRAPHS of these functions? They intersect at (0, 0) and (1, 1).
Also, the square root function is a reflection of the part of the quadratic function where x is greater than or equal to 0, about y = x.
­ Why do they intersect at (0,0) and (1,1) ? 3
Aim#56GraphingCubeRootSquareRootCubicFunctions.notebook
February 25, 2015
Example #2: Create a data table for y = x3 and and graph both functions on the same set of axes. Round decimal answers to the nearest hundredth. Domain of y = x3 is:
_______________
Range of y = x3 is:
_______________
Domain of is: ________________
Range of is: _______________
Using the table and graphs, what observations can you make about the relationships between y = x3 and ?
(How are they related, describe their symmetry, etc.)
They share the points (0, 0), (1, 1), (­1, ­1).
The domain and range of both functions are all Real #'s.
The functions are symmetrical to the Origin.
One is a reflection of the other in the line y = x again.
4
Aim#56GraphingCubeRootSquareRootCubicFunctions.notebook
February 25, 2015
Summary 5