SAT II Math II : Range and Domain

Study concepts, example questions & explanations for SAT II Math II

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Example Questions

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Example Question #1 : Range And Domain

Define .

Give the range of .

Possible Answers:

The correct range is not among the other responses.

Correct answer:

The correct range is not among the other responses.

Explanation:

The function can be rewritten as follows:

The expression  can assume any value except for 0, so the expression  can assume any value except for 1. The range is therefore the set of all real numbers except for 1, or

.

This choice is not among the responses.

Example Question #2 : Range And Domain

Define .

Give the domain of .

Possible Answers:

Correct answer:

Explanation:

In a rational function, the domain excludes exactly the value(s) of the variable which make the denominator equal to 0. Set the denominator to find these values:

The domain is the set of all real numbers except 7 - that is, .

Example Question #3 : Range And Domain

Define 

Give the domain of

Possible Answers:

Correct answer:

Explanation:

Every real number has one real cube root, so there are no restrictions on the radicand of a cube root expression. The domain is the set of all real numbers.

Example Question #4 : Range And Domain

Define 

Give the range of .

Possible Answers:

Correct answer:

Explanation:

 for any real value of .

Therefore,

The range is .

Example Question #5 : Range And Domain

Define 

Give the range of .

Possible Answers:

Correct answer:

Explanation:

 for any real value of , so

,

making the range .

Example Question #3 : Range And Domain

Define .

Give the range of 

Possible Answers:

Correct answer:

Explanation:

The radicand within a square root symbol must be nonnegative, so

This happens if and only if , so the domain of  is .

 

 assumes its greatest value when , which is the point on  where  is least - this is at .

 

 

Similarly,  assumes its least value when , which is the point on  where  is greatest - this is at .

 

Therefore, the range of  is .

Example Question #7 : Range And Domain

Define 

Give the range of .

Possible Answers:

Correct answer:

Explanation:

 can be rewritten as .

For all real values of ,

 or .

Therefore,

 or  and

 or  .

The range of  is .

Example Question #4 : Range And Domain

What is the domain of the function 

Possible Answers:

Correct answer:

Explanation:

The domain of a function is all the x-values that in that function. The function  is a upward facing parabola with a vertex as (0,3). The parabola keeps getting wider and is not bounded by any x-values so it will continue forever. Parenthesis are used because infinity is not a definable number and so it can not be included.

Example Question #5 : Range And Domain

What is the domain of the function?   

Possible Answers:

Correct answer:

Explanation:

Notice this function resembles the parent function .  The value of  must be zero or greater.

Set up an inequality to determine the domain of .

Subtract three from both sides.

Divide by negative ten on both sides.  The sign will switch.

The domain is:  

Example Question #6 : Range And Domain

What is the range of the function ?

Possible Answers:

All real numbers.

All real numbers except .

All real numbers except .

All real numbers except .

Correct answer:

All real numbers except .

Explanation:

Start by considering the term  will hold for all values of , except when . Thus,  must be defined by all values except  since the equation is just shifted down by .

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