Graphing Square and Cube Roots 4 - MRS. KUNZLERmrskunzler.weebly.com/uploads/5/6/7/2/56722655/4.7...64 Graphing Square Root and Cube Root Functions Example 7) โGraph (๐ฅ)= ๐ฅโ3+2
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Graphing Square and Cube Roots {4.7} Standard: F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. Standard: F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
b) Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Compare and contrast square root, cubed root, and step functions with all other functions.
Standard: F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.
Lingo: Radical
Square root
โ Cube root
โ 3
The Parent Fucntions
Sq
ua
re
Ro
ots
๐(๐ฅ) = โ๐ฅ
x Work y (x,y)
0 โ๐ = ๐ 0 (0, 0)
1 โ๐ = ๐ 1 (1, 1)
4 โ๐ = ๐ 2 (4, 2)
9 โ๐ = ๐ 3 (9, 3)
Domain: [0, โ)
Range: [0, โ)
Cu
be
Ro
ots
๐(๐ฅ) = โ๐ฅ3
x Work y (x,y)
-1 โโ๐๐
= โ๐ -1 (-1, -1)
0 โ๐๐
= ๐ 0 (0, 0)
1 โ๐๐
= ๐ 1 (1, 1)
Domain: (โโ, โ)
Range: (โโ, โ)
radical
index
Starting Point
Center Point
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Graphing Square and Cube Roots Cont. {4.7} Transformation Review
๐(๐ฅ โ ๐) or โ๐ฅ โ ๐
Moves the parent function
OR
*Remember! If it โliesโ inside the parenthesis
or โliesโ underneath the radical, it ____ lies
____to you.
๐(๐ฅ) + ๐ or โ๐ฅ + ๐
Moves the parent function
OR
โ๐(๐ฅ) or โโ๐ฅ
over the x-axis
๐(โ๐ฅ) or โโ๐ฅ
over the y-axis
Example 1) Given ๐(๐ฅ) = โ๐ฅ describe the transformation of ๐(๐ฅ + 3).
Left 3
Example 2) How has ๐(๐ฅ) = โ๐ฅ โ 2 + 10 transformed from the parent function?
Right 2 and up 10
Example 3) Given ๐(๐ฅ) = โ๐ฅ3
describe the transformation of ๐(โ๐ฅ) โ 8. Reflection over the x-axis and down 8
Example 4) How has ๐(๐ฅ) = โโ๐ฅ + 53
+ 4 transformed from the parent function? Reflection over the y-axis, left 5, and up 4.
Example 5) Given ๐(๐ฅ) = โ๐ฅ describe the transformation of ๐(๐ฅ โ 5) โ 1.
Right 5 and down 1
Example 6) How has ๐(๐ฅ) = โ๐ฅ3
+ 8 transformed from the parent function? up 8
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Graphing Square Root and Cube Root Functions
Example 7) Graph ๐(๐ฅ) = โ๐ฅ โ 3 + 2
Steps to Graphing:
Step 1 Identify the transformation
Step 2 Move the x and y-axis up/down or right/left
based on step 1.
Step 3 Identify the points of the parent function
Step 4 If the transformation has a reflection, use the
chart below.
Reflection over x-axis Reflection over y-axis
Switch all the signs of the y-values
Switch all the signs of the x-values
Step 5 Graph the parent function using your โnewโ x
and y-axis
x y
0 0
1 1
4 2
9 3
What is the domain of the function above?
[3, โ) What is the range of the function above?
[2, โ)
Transformation:
3 Right and Up 2
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Graphing Square and Cube Roots Cont. {4.7} Example 8) Graph ๐(๐ฅ) = โโ๐ฅ + 1 โ 2 x y
0 0
1 -1
4 -2
9 -3
Transformation: left 1 and down 2 and reflects over x-
axis
Domain: [โ1, โ)
Range: [โ2, โ)
Example 9) Graph ๐(๐ฅ) = โ๐ฅ โ 13
+ 2 Transformation: right 1 and up 2
x y
-1 -1
0 0
1 1
Domain:(โโ, โ) or all real
numbers
Range:(โโ, โ) or all real numbers
Example 10) ๐(๐ฅ + 1) โ 3
a) Describe the transformation that will occur to the parent function ๐(๐ฅ).
Left 1 and down 3
b) Graph the transformed function on the graph to the right using the parent function given.
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Example 11) โ๐(๐ฅ + 3) โ 2
c) Describe the transformation that will occur to the parent function ๐(๐ฅ).
Reflect over the x-axis, Left 3 and down 2
Example 12) Graph the transformed function on
the graph to the right using the parent function given.
Example 13) Write an equation for the function ๐(๐ฅ) = โ๐ฅ by transforming the equation as described below:
Translated to the right 7, up 4, and reflected over the y-axis
๐(๐ฅ) = โโ(๐ฅ โ 7) + 4
Example 14) Write an equation to the graph to the right.
๐(๐ฅ) = โ๐ฅ โ 1 + 1
Example 15) Write an equation to the graph to the right.
๐(๐ฅ) = โ๐ฅ + 23
+ 4
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