aim: applications of functions? hw p. 27 #74, 76, 77, functions worksheet #1-3 1 expressing a...
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
Expressing a quantity as a function of another quantity.
Do Now: Express the area, A, of a circle as a function of its circumference.
i.e. Write an Area formula in terms of C.2A r 2C r
2
Cr
2
2
CA
2
2
CA C
2
2 22
CA C
2
24
CA C
2
4
CA C
Write the radius in terms of the circumference and then substitute that radius into the Area equation.
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
Expressing a quantity as a function of another quantity.
Equal squares are cut from the corners of a rectangular piece of cardboard 5 ft wide and 7 ft long. The sides are then folded up to form a box with no top.
1. Express the volume of the box as a function of the width of the squares that are cut out.
2. What is the domain of this function?
5
7
x
x
5 2 7 2V x x x 5 2 7 2 0
0 2.5
x x x
x
7 2
5 2
V L W H
L x
W x
H x
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
Expressing a quantity as a function of another quantity.
A square is 24 cm on each side. Equal squares are then cut from each corner and folded up to make a box with no top.
1. Express the volume of the box as a function of the width of the squares that are cut out.
2. What is the domain of this function?
24
24
x
x
224 2 24 2
24 2
V x x x
V x x
224 2 0
0 12
x x x
x
24 2
24 2
V L W H
L x
W x
H x
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
Function Worksheet #1-3
1. A farmer uses 80 ft. of fencing to make four sides of a rectangular pen. Express the area of the pen as a function of the length of the pen. What is the domain of this-function?
2. A woman is designing a rectangular garden that will have an area of 400 sq.ft. She needs to know how much fencing would be required for various dimensions of the garden: Let P(w) denote the perimeter of the garden if its width is w feet. Give a formula for the function P. What is it domain?
3. Express the area of a rectangle inscribed in a circle of radius 10 as a function of its width.
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
The function has positive x and y-values within this domain
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3
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AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3