Square Root Function (MAS506).notebook
February 23, 2017
Example: Determine the rule.
y
5
4
3
2
1
x
­10 ­9 ­8 ­7 ­6 ­5 ­4 ­3 ­2 ­1­10 1 2 3 4 5 6
­2
­3
­4
­5
­6
­7
­8
­9
­10
­11
­12
­13
­14
­15
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Square Root Function (MAS506).notebook
February 23, 2017
Zeros and Sign of the Square Root Function
Example: The hull of a ship follows the curve of the
function
for a length of 18m. The water line
corresponds to the x-axis.
a)
What interval represents the part of
the hull that is above the water line?
2
Square Root Function (MAS506).notebook
February 23, 2017
a)
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Square Root Function (MAS506).notebook
February 23, 2017
b) When carrying a full cargo, the equation
becomes
.
What interval represents the portion of the
hull below the water line?
4
Square Root Function (MAS506).notebook
Determine the zero of the function
February 23, 2017
.
5
Square Root Function (MAS506).notebook
February 23, 2017
Example: After one month in operation, a company's
revenue has grown according to the square
root function shown.
Losses amounted to
$4 million the first
month. After ten
months, a $5 million
profit was recorded.
y
6
(10 ,
5)
5
4
3
2
1
x
0
1
2
3
4
5
6
7
8
9
10 11 12
­1
­2
­3
­4
(1 ,
­4)
­5
After how many months in operation did the
company begin to make a profit?
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Square Root Function (MAS506).notebook
February 23, 2017
7
Square Root Function (MAS506).notebook
February 23, 2017
If
a) What are the domain and range of f ?
b) Draw the graph of f.
a)
b)
Dom:
y
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
Ran:
­14
­12
­10
­8
­6
­4
­2
x
0
2
4
­2
­3
­4
­5
­6
­7
­8
8
Square Root Function (MAS506).notebook
February 23, 2017
Provide a study of the following function.
Dom:
Ran:
Inc:
Dec:
Pos:
Neg:
Zero:
y-int:
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Square Root Function (MAS506).notebook
February 23, 2017
Inverse of the Square Root Function
Example:
What is the rule of the inverse of the
function
Dom f:
Dom f ­1 :
Ran f:
Ran f ­1:
10
Square Root Function (MAS506).notebook
February 23, 2017
isolate y
or
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Square Root Function (MAS506).notebook
February 23, 2017
Examples:
Given
, sketch the inverse and find
its rule.
y
10
9
8
7
6
5
4
(5 ,
3)
3
2
1
x
(6 ,
­0)
­5 ­4 ­3 ­2 ­1 0
­1
1
2
3
4
5
6
7
8
9 10
­2
­3
(9 ,
­3)
­4
­5
­6
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Square Root Function (MAS506).notebook
February 23, 2017
y
10
9
8
7
6
5
4
3
2
1
­5 ­4 ­3 ­2 ­1­10
­2
­3
­4
­5
­6
­7
­8
Determine...
a) the rule of the function.
x
1
2
3
4
5
6
7
8
9 10
b) the rule of the inverse
c) the domain and range
of the inverse.
Sketch the inverse
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Square Root Function (MAS506).notebook
February 23, 2017
14