Maths Quest Maths B Year 11 for Queenslandchapter 2 Relations and Functions Worksheet 2.21
Maths Quest Maths B Year 11 for QueenslandChapter 2 Relations and Functions WorkSHEET 2.21
WorkSHEET 2.2Relations and functionsName: ______
Maths Quest Maths B Year 11 for QueenslandChapter 2 Relations and Functions WorkSHEET 2.21
1 / Consider the following sets of coordinates and determine the type of relation for each.(a){(3, 2), (4, 2), (3, 2), (4, 2)}
(b){(1, 1), (1, 3), (1, 5)}
(c){(2, 3), (3, 3), (4, 3)}
(d){(1, 1), (2, 2), (3, 3)} / (a)many-to-many relation (as x-values double up and y-values double up)
(b)one-to-many relation (as one x-value corresponds to many y-values)
(c)many-to-one relation (as many x-values correspond to one y-value)
(d)one-to-one relation (a different x-value to each y-value) / 1
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2 / Consider the following equations and determine the type of relation for each.
(a)
(b)
(c)
(d) / (a) (a parabola)
many-to-one relation
(b) (straight line)
one-to-one-relation
(c) (circle)
many-to-many relation
(d)
(a parabola, symmetrical about x-axis)
one-to-many relation / 1
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3 / Which of the relations in question 2 are functions? / Only parts (a) and (b) are functions.
(Only one-to-one and many-to-one relations are functions.) / 1
4 / If and , find:
(a)
(b)
(c)
(d) / (a)
(b)
(c)
(d)
/ 1
1
1
1
1
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5 / If and , find:
(a)
(b) / (a)
(b)
/ 1
1
1
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6 / State the domain, co-domain and range for the following.
(a)
(b) / (a)
The domain is given as R.
The co-domain is given as R.
As the parabola depicted has a minimum turning point at (1, 0), the range is [0, )
(b)
The domain is given as (1,).
The co-domain is given as R.
As the graph depicted rises steeply as x gets smaller and closer to 1. As the
x-values get large the graph approaches the x-axis. Therefore the range is (0, ) / 1
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7 / What is the maximal domain and range for each of the following?
(a)
(b) / (a). As the square root only accepts values 0, then
Domain is [2.5, )
When x = 2.5, y = 0, which is the minimum value for y.
Range is [0, )
(b)
The fraction is undefined when the denominator is zero.
Domain is R \ {0.25}
Range is R \ {0}as the two parts of the graph never cross the y-axis. / 1
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8 / Which of the following graphs are one-to-one functions?
(a)
(b)
(c)
(d)
(e) / Only (c) and (e) are one-to-one functions.
[(a), (b) and (d) correspond to many-to-one functions as a horizontal line on each graph will pass through more than one x-value.] / 2
9 / Break the following many-to-one functions into two separate, maximal domains so that each part is a one-to-one function.
(a)
(b)
(c) / (a)
This parabola is symmetrical about the
y-axis, so the two possible maximal domains are: [0, ) and (, 0).
(b)
This shape is symmetrical about the
y-axis, so the two possible maximal domains are: [0, ) and (, 0).
(c)
This shape is symmetrical about the
y-axis, so the two possible maximal domains are: [0, ) and (, 0). / 1
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10 / If
(a)State the range of f.
(b)Find f(1), f(2) and f(3). / (a)As the two separate parts of the graph connect, the range is R.
(b)f(1) = 2 1 = 1
f(2) = 2 2 = 0
f(3) = 4 3 3 = 5 / 1
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