Functions/Series - GMAT Quantitative
Card 1 of 688
There exists a set 
= {1, 2, 3, 4}. Which of the following defines a function of 
?
There exists a set
Tap to reveal answer
Let's look at 
and see if any of them are functions.
1. 
= {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of 
because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.
2. 
= {(3, 1), (4, 2), (1, 1)}: This cannot be a function of 
because it contains no ordered pair with first coordinate 2. Because the set 
= {1, 2, 3, 4}, we need an ordered pair of the form (2, ) .
3. 
= {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function. Even though two of the ordered pairs have the same number (2) as the first coordinate, 
is still a function of 
because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.
Let's look at
1.
2.
3.
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Which of the following would be a valid alternative definition of the function
?
Which of the following would be a valid alternative definition of the function
Tap to reveal answer
If 
, then 
and 
are both positive, so
If 
, then , then 
is positive and 
is negative, so
If 
, then 
and 
are both negative, so
If
If
If
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Which of the following would be a valid alternative definition of the function
?
Which of the following would be a valid alternative definition of the function
Tap to reveal answer
If , then and are both positive, so
If , then , then is positive and is negative, so
If , then and are both negative, so
If
If
If
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Define &space;=&space;2x&space;-&space;%7Cx%7C "g(x) = 2x - |x|")
.
Which of the following would be a valid alternative way of expressing the definition of 
?
Define
Which of the following would be a valid alternative way of expressing the definition of
Tap to reveal answer
If 
, then 
,and subsequently, 
If 
, then 
,and subsequently, 
If
If
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There exists a set = {1, 2, 3, 4}. Which of the following defines a function of ?
There exists a set
Tap to reveal answer
Let's look at and see if any of them are functions.
1. = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.
2. = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of because it contains no ordered pair with first coordinate 2. Because the set = {1, 2, 3, 4}, we need an ordered pair of the form (2, ) .
3. = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function. Even though two of the ordered pairs have the same number (2) as the first coordinate, is still a function of because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.
Let's look at
1.
2.
3.
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There exists a set = {1, 2, 3, 4}. Which of the following defines a function of ?
There exists a set
Tap to reveal answer
Let's look at and see if any of them are functions.
1. = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.
2. = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of because it contains no ordered pair with first coordinate 2. Because the set = {1, 2, 3, 4}, we need an ordered pair of the form (2, ) .
3. = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function. Even though two of the ordered pairs have the same number (2) as the first coordinate, is still a function of because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.
Let's look at
1.
2.
3.
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There exists a set = {1, 2, 3, 4}. Which of the following defines a function of ?
There exists a set
Tap to reveal answer
Let's look at and see if any of them are functions.
1. = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.
2. = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of because it contains no ordered pair with first coordinate 2. Because the set = {1, 2, 3, 4}, we need an ordered pair of the form (2, ) .
3. = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function. Even though two of the ordered pairs have the same number (2) as the first coordinate, is still a function of because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.
Let's look at
1.
2.
3.
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There exists a set = {1, 2, 3, 4}. Which of the following defines a function of ?
There exists a set
Tap to reveal answer
Let's look at and see if any of them are functions.
1. = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.
2. = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of because it contains no ordered pair with first coordinate 2. Because the set = {1, 2, 3, 4}, we need an ordered pair of the form (2, ) .
3. = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function. Even though two of the ordered pairs have the same number (2) as the first coordinate, is still a function of because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.
Let's look at
1.
2.
3.
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There exists a set = {1, 2, 3, 4}. Which of the following defines a function of ?
There exists a set
Tap to reveal answer
Let's look at and see if any of them are functions.
1. = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.
2. = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of because it contains no ordered pair with first coordinate 2. Because the set = {1, 2, 3, 4}, we need an ordered pair of the form (2, ) .
3. = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function. Even though two of the ordered pairs have the same number (2) as the first coordinate, is still a function of because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.
Let's look at
1.
2.
3.
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There exists a set = {1, 2, 3, 4}. Which of the following defines a function of ?
There exists a set
Tap to reveal answer
Let's look at and see if any of them are functions.
1. = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.
2. = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of because it contains no ordered pair with first coordinate 2. Because the set = {1, 2, 3, 4}, we need an ordered pair of the form (2, ) .
3. = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function. Even though two of the ordered pairs have the same number (2) as the first coordinate, is still a function of because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.
Let's look at
1.
2.
3.
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.
Evaluate 
.
Evaluate
Tap to reveal answer
First we evaluate 
. Since the parameter is negative, we use the first half of the definition of 
:
; since the parameter here is again negative, we use the first half of the definition of 
:
Therefore, 
.
First we evaluate
Therefore,
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.
Evaluate .
Evaluate
Tap to reveal answer
First we evaluate . Since the parameter is negative, we use the first half of the definition of :
; since the parameter here is again negative, we use the first half of the definition of :
Therefore, .
First we evaluate
Therefore,
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.
Evaluate .
Evaluate
Tap to reveal answer
First we evaluate . Since the parameter is negative, we use the first half of the definition of :
; since the parameter here is again negative, we use the first half of the definition of :
Therefore, .
First we evaluate
Therefore,
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Define 
. Which of the following would be a valid alternative way of expressing the definition of 
?
Define
Tap to reveal answer
By definition:
If 
, then 
,and subsequently, 
If 
, then 
,and subsequently, 
By definition:
If
If
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Define .
Which of the following would be a valid alternative way of expressing the definition of ?
Define
Which of the following would be a valid alternative way of expressing the definition of
Tap to reveal answer
If , then ,and subsequently,
If , then ,and subsequently,
If
If
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There exists a set = {1, 2, 3, 4}. Which of the following defines a function of ?
There exists a set
Tap to reveal answer
Let's look at and see if any of them are functions.
1. = {(2, 3), (1, 4), (2, 1), (3, 2), (4, 4)}: This cannot be a function of because two of the ordered pairs, (2, 3) and (2, 1) have the same number (2) as the first coordinate.
2. = {(3, 1), (4, 2), (1, 1)}: This cannot be a function of because it contains no ordered pair with first coordinate 2. Because the set = {1, 2, 3, 4}, we need an ordered pair of the form (2, ) .
3. = {(2, 1), (3, 4), (1, 4), (2, 1), (4, 4)}: This is a function. Even though two of the ordered pairs have the same number (2) as the first coordinate, is still a function of because (2, 1) is simply repeated twice, so the two ordered pairs with first coordinate 2 are equal.
Let's look at
1.
2.
3.
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Define . Which of the following would be a valid alternative way of expressing the definition of ?
Define
Tap to reveal answer
By definition:
If , then ,and subsequently,
If , then ,and subsequently,
By definition:
If
If
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Define . Which of the following would be a valid alternative way of expressing the definition of ?
Define
Tap to reveal answer
By definition:
If , then ,and subsequently,
If , then ,and subsequently,
By definition:
If
If
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Which of the following would be a valid alternative definition of the function
?
Which of the following would be a valid alternative definition of the function
Tap to reveal answer
If , then and are both positive, so
If , then , then is positive and is negative, so
If , then and are both negative, so
If
If
If
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Define .
Which of the following would be a valid alternative way of expressing the definition of ?
Define
Which of the following would be a valid alternative way of expressing the definition of
Tap to reveal answer
If , then ,and subsequently,
If , then ,and subsequently,
If
If
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