Graphing a function - GMAT Quantitative
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What is the domain of y = 4 - $x^{2}$?
What is the domain of y = 4 - $x^{2}$?
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The domain of the function specifies the values that 
can take. Here, $4-x^{2}$ is defined for every value of 
, so the domain is all real numbers.
The domain of the function specifies the values that
What is the domain of y=-2$\sqrt{x}$?
What is the domain of y=-2$\sqrt{x}$?
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To find the domain, we need to decide which values 
can take. The 
is under a square root sign, so 
cannot be negative. 
can, however, be 0, because we can take the square root of zero. Therefore the domain is xgeq 0.
To find the domain, we need to decide which values
What is the domain of the function $y=$\sqrt{4-x^{2}$$}?
What is the domain of the function $y=$\sqrt{4-x^{2}$$}?
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To find the domain, we must find the interval on which $$\sqrt{4-x^{2}$$} is defined. We know that the expression under the radical must be positive or 0, so $$\sqrt{4-x^{2}$$} is defined when $x^{2}$leq 4. This occurs when x geq -2 and x leq 2. In interval notation, the domain is 
.
To find the domain, we must find the interval on which $$\sqrt{4-x^{2}$$} is defined. We know that the expression under the radical must be positive or 0, so $$\sqrt{4-x^{2}$$} is defined when $x^{2}$leq 4. This occurs when x geq -2 and x leq 2. In interval notation, the domain is
Define the functions 
and 
as follows:
What is the domain of the function 
?
Define the functions
What is the domain of the function
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The domain of 
is the intersection of the domains of 
and 
. 
and 
are each restricted to all values of 
that allow the radicand 
to be nonnegative - that is,
, or
Since the domains of 
and 
are the same, the domain of 
is also the same. In interval form the domain of 
is 
The domain of
Since the domains of
Define 
.
What is the natural domain of 
?
Define
What is the natural domain of
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The only restriction on the domain of 
is that the denominator cannot be 0. We set the denominator to 0 and solve for 
to find the excluded values:
The domain is the set of all real numbers except those two - that is,
.
The only restriction on the domain of
The domain is the set of all real numbers except those two - that is,
Define 
What is the natural domain of 
?
Define
What is the natural domain of
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The radical in and of itself does not restrict the domain, since every real number has a real cube root. However, since the expression 
is in a denominator, it cannot be equal to zero, so the domain excludes the value(s) for which
27 is the only number excluded from the domain.
The radical in and of itself does not restrict the domain, since every real number has a real cube root. However, since the expression
27 is the only number excluded from the domain.
Define 
What is the natural domain of 
?
Define
What is the natural domain of
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Since the expression 
is in a denominator, it cannot be equal to zero, so the domain excludes the value(s) for which 
. We solve for 
by factoring the polynomial, which we can do as follows:
Replacing the question marks with integers whose product is 
and whose sum is 3:
Therefore, the domain excludes these two values of 
.
Since the expression
Replacing the question marks with integers whose product is
Therefore, the domain excludes these two values of
What is the domain of y = 4 - $x^{2}$?
What is the domain of y = 4 - $x^{2}$?
Tap to see back →
The domain of the function specifies the values that can take. Here, $4-x^{2}$ is defined for every value of , so the domain is all real numbers.
The domain of the function specifies the values that
What is the domain of y=-2$\sqrt{x}$?
What is the domain of y=-2$\sqrt{x}$?
Tap to see back →
To find the domain, we need to decide which values can take. The is under a square root sign, so cannot be negative. can, however, be 0, because we can take the square root of zero. Therefore the domain is xgeq 0.
To find the domain, we need to decide which values
What is the domain of the function $y=$\sqrt{4-x^{2}$$}?
What is the domain of the function $y=$\sqrt{4-x^{2}$$}?
Tap to see back →
To find the domain, we must find the interval on which $$\sqrt{4-x^{2}$$} is defined. We know that the expression under the radical must be positive or 0, so $$\sqrt{4-x^{2}$$} is defined when $x^{2}$leq 4. This occurs when x geq -2 and x leq 2. In interval notation, the domain is .
To find the domain, we must find the interval on which $$\sqrt{4-x^{2}$$} is defined. We know that the expression under the radical must be positive or 0, so $$\sqrt{4-x^{2}$$} is defined when $x^{2}$leq 4. This occurs when x geq -2 and x leq 2. In interval notation, the domain is
Define the functions and as follows:
What is the domain of the function ?
Define the functions
What is the domain of the function
Tap to see back →
The domain of is the intersection of the domains of and . and are each restricted to all values of that allow the radicand to be nonnegative - that is,
, or
Since the domains of and are the same, the domain of is also the same. In interval form the domain of is
The domain of
Since the domains of
Define .
What is the natural domain of ?
Define
What is the natural domain of
Tap to see back →
The only restriction on the domain of is that the denominator cannot be 0. We set the denominator to 0 and solve for to find the excluded values:
The domain is the set of all real numbers except those two - that is,
.
The only restriction on the domain of
The domain is the set of all real numbers except those two - that is,
Define
What is the natural domain of ?
Define
What is the natural domain of
Tap to see back →
The radical in and of itself does not restrict the domain, since every real number has a real cube root. However, since the expression is in a denominator, it cannot be equal to zero, so the domain excludes the value(s) for which
27 is the only number excluded from the domain.
The radical in and of itself does not restrict the domain, since every real number has a real cube root. However, since the expression
27 is the only number excluded from the domain.
Define
What is the natural domain of ?
Define
What is the natural domain of
Tap to see back →
Since the expression is in a denominator, it cannot be equal to zero, so the domain excludes the value(s) for which . We solve for by factoring the polynomial, which we can do as follows:
Replacing the question marks with integers whose product is and whose sum is 3:
Therefore, the domain excludes these two values of .
Since the expression
Replacing the question marks with integers whose product is
Therefore, the domain excludes these two values of
What is the domain of y = 4 - $x^{2}$?
What is the domain of y = 4 - $x^{2}$?
Tap to see back →
The domain of the function specifies the values that can take. Here, $4-x^{2}$ is defined for every value of , so the domain is all real numbers.
The domain of the function specifies the values that
What is the domain of y=-2$\sqrt{x}$?
What is the domain of y=-2$\sqrt{x}$?
Tap to see back →
To find the domain, we need to decide which values can take. The is under a square root sign, so cannot be negative. can, however, be 0, because we can take the square root of zero. Therefore the domain is xgeq 0.
To find the domain, we need to decide which values
What is the domain of the function $y=$\sqrt{4-x^{2}$$}?
What is the domain of the function $y=$\sqrt{4-x^{2}$$}?
Tap to see back →
To find the domain, we must find the interval on which $$\sqrt{4-x^{2}$$} is defined. We know that the expression under the radical must be positive or 0, so $$\sqrt{4-x^{2}$$} is defined when $x^{2}$leq 4. This occurs when x geq -2 and x leq 2. In interval notation, the domain is .
To find the domain, we must find the interval on which $$\sqrt{4-x^{2}$$} is defined. We know that the expression under the radical must be positive or 0, so $$\sqrt{4-x^{2}$$} is defined when $x^{2}$leq 4. This occurs when x geq -2 and x leq 2. In interval notation, the domain is
Define the functions and as follows:
What is the domain of the function ?
Define the functions
What is the domain of the function
Tap to see back →
The domain of is the intersection of the domains of and . and are each restricted to all values of that allow the radicand to be nonnegative - that is,
, or
Since the domains of and are the same, the domain of is also the same. In interval form the domain of is
The domain of
Since the domains of
Define .
What is the natural domain of ?
Define
What is the natural domain of
Tap to see back →
The only restriction on the domain of is that the denominator cannot be 0. We set the denominator to 0 and solve for to find the excluded values:
The domain is the set of all real numbers except those two - that is,
.
The only restriction on the domain of
The domain is the set of all real numbers except those two - that is,
Define
What is the natural domain of ?
Define
What is the natural domain of
Tap to see back →
The radical in and of itself does not restrict the domain, since every real number has a real cube root. However, since the expression is in a denominator, it cannot be equal to zero, so the domain excludes the value(s) for which
27 is the only number excluded from the domain.
The radical in and of itself does not restrict the domain, since every real number has a real cube root. However, since the expression
27 is the only number excluded from the domain.