7.5 Graphing Square Root & Cube Root Functions By: L. Keali’i Alicea.
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7.5 Graphing 7.5 Graphing Square Root & Square Root & Cube Root Cube Root Functions Functions By: L. Keali’i By: L. Keali’i Alicea Alicea
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Transcript of 7.5 Graphing Square Root & Cube Root Functions By: L. Keali’i Alicea.
7.5 Graphing 7.5 Graphing Square Root & Square Root &
Cube Root Cube Root FunctionsFunctions
By: L. Keali’i By: L. Keali’i AliceaAlicea
First, let’s look at the First, let’s look at the graphs of a square root graphs of a square root
function.function.xy
0, 0
1, 1
4, 2
9, 3
16, 4
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 2 4 6 8 10 12 14 16 18
0, 0
1, 2
4, 4
9, 6
16, 8
25, 10
0
2
4
6
8
10
12
0 5 10 15 20 25 30
xy 2
xay Always goes thru the points (0,0) and (1,a).
-27, -3
-8, -2
-1, -1
0, 0
1, 1
8, 2
27, 3
-4
-3
-2
-1
0
1
2
3
4
-30 -20 -10 0 10 20 30
3 xy -27, 9
-8, 6
-1, 3
0, 0
1, -3
8, -6
27, -9-10
-8
-6
-4
-2
0
2
4
6
8
10
-30 -20 -10 0 10 20 30
33 xy
Now, let’s look at the graphs Now, let’s look at the graphs of a cube root function.of a cube root function.
3 xay Always goes thru the points (-1,-a), (0,0), and (1,a).
GeneralizationGeneralization
xay 3 xay
Always goes thru the points (0,0) and (1,a).
Always goes thru the points (-1,-a), (0,0), and (1,a).
Ex: GraphEx: Graph xy 4
Goes thru the points (0,0) and (1,a).
Since a=-4, the graph will pass thru (0,0) and (1,-4)
0, 0
1, -4
9, -12
16, -16
25, -20
-25
-20
-15
-10
-5
0
0 5 10 15 20 25 30
Now, what happens when there are Now, what happens when there are numbers added or subtracted numbers added or subtracted
inside and/or outside the radical?inside and/or outside the radical?
khxaykhxay 3or
Step 1: Find points on the parent graph
Step 2: Shift these points h units horizontally (use opposite sign) and k units vertically (use same sign).
3or xayxay
Ex: Describe how to obtain the Ex: Describe how to obtain the graph of from the graph ofgraph of from the graph of 123 xy 3 xy
Shift all the points from
To the right 2 and up 1.
3 xy
Ex: GraphEx: Graph 142 xy
x y
0 0
1 2
4 4
9 6
xyfortable 2 Now, shift these points to the left 4 and down 1.
x y
-4 -1
-3 1
0 3
5 5
-4, -1
-3, 1
0, 3
5, 5
-2
-1
0
1
2
3
4
5
6
-6 -4 -2 0 2 4 6
(x-value – 4)
(y-value -1)
Ex: GraphEx: Graph 2323 xy
32 xyfortable
x y
-27 6
-8 4
-1 2
0 0
1 -2
8 -4
27 -6
Now, shift these points to the right 3 and up 2.
(x-value + 3)(y-value + 2)
x y
-24 8
-5 6
2 4
3 2
4 0
11 -2
30 -4
-24, 8
-5, 6
2, 4
3, 2
4, 0
11, -2
30, -4
-6
-4
-2
0
2
4
6
8
10
-30 -20 -10 0 10 20 30 40
Ex: State the domain and range of Ex: State the domain and range of the functions in the last 2 the functions in the last 2
examples.examples.142 xy
-4, -1
-3, 1
0, 3
5, 5
-2
-1
0
1
2
3
4
5
6
-6 -4 -2 0 2 4 6
-24, 8
-5, 6
2, 4
3, 2
4, 0
11, -2
30, -4
-6
-4
-2
0
2
4
6
8
10
-30 -20 -10 0 10 20 30 40
2323 xy
x-values y-values
Domain:Domain:
Range:Range:
Domain:Domain:
Range:Range:
4x1y
numbersrealall numbersrealall
The graph doesn’t have a beginning or ending point.
(Meaning all x & y-values are possible.)
The graph has a beginning point of (-4,-1).
AssignmentAssignment 7.5 A (1-6, 7-23 odd, 25-27)7.5 A (1-6, 7-23 odd, 25-27)
