All GMAT Math Resources
Example Questions
Example Question #1 : Graphing A Function
What is the domain of ?
all real numbers
all real numbers
The domain of the function specifies the values that can take. Here, is defined for every value of , so the domain is all real numbers.
Example Question #2 : Graphing A Function
What is the domain of ?
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 .
Example Question #3 : Graphing A Function
What is the domain of the function ?
To find the domain, we must find the interval on which is defined. We know that the expression under the radical must be positive or 0, so is defined when . This occurs when and . In interval notation, the domain is .
Example Question #3 : Graphing A Function
Define the functions and as follows:
What is the domain of the function ?
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
Example Question #4 : How To Graph A Function
Define
What is the natural domain of ?
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.
Example Question #5 : Graphing A Function
Define
What is the natural domain of ?
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 .
Example Question #217 : Advanced Geometry
Define .
What is the natural domain of ?
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,
.