Algebra 1 : How to find the domain of a function

Study concepts, example questions & explanations for Algebra 1

varsity tutors app store varsity tutors android store

Example Questions

Example Question #21 : How To Find The Domain Of A Function

What is the domain of the function shown here?  

Possible Answers:

: All real numbers

Correct answer:

Explanation:

Begin by factoring the denominator to get: 

.

Do not simplify further! Realize that any value of "x" that causes the denominator to equal zero is not included in the domain of the function.

Therefore, one can see that the domain does not include x values of 8 or -2. No other gaps exist in this function so one can definitively say the domain is characterized by .

Example Question #21 : How To Find The Domain Of A Function

What is the domain of ?

Possible Answers:

Correct answer:

Explanation:

The value of the inner term of a square root cannot be negative.  This means that no number can be less than zero.

Set the inner term equal to zero and solve for .

This means that  cannot be less than this value.

Therefore, the  exists for every number equal to  or greater.

The answer is:  

Example Question #21 : How To Find The Domain Of A Function

What is the domain of 

Possible Answers:

Correct answer:

Explanation:

The terms inside a square root cannot be negative, but can be equal to zero.

Set the terms inside the square root to zero to determine where the domain will begin.  

The value of  cannot be less than negative two, but can be more than negative two.  The negative sign in front of the square root symbol will flip the graph across the x-axis, and will not affect the domain.  

The domain is:  

Example Question #24 : How To Find The Domain Of A Function

Find the domain of the following function:

Possible Answers:

Correct answer:

Explanation:

In determining the domain of a function, we must ask ourselves where the function is undefined. To do this for our function, we must set the denominator equal to zero, and solve for x; at this x value, we get a zero in the denominator of the function which produces an undefined value.

This is the only limitation for the domain of the function, so our domain is

Example Question #25 : How To Find The Domain Of A Function

Find the domain of:  

Possible Answers:

Correct answer:

Explanation:

The contents inside the square root cannot be less than zero.

Set the inner quantity equal to zero. 

Find .  This is the critical point.  Add  on both sides and then divide by two on both sides.

We will test numbers less than and more three halves.

Let:  

Let:  

The negative inside the square square root indicates that this is an imaginary term.

This tells us that the domain is satisfied when  is less than or equal to .

The correct answer is:  

Example Question #26 : How To Find The Domain Of A Function

Give the domain of the function

Possible Answers:

The set of all real numbers

Correct answer:

Explanation:

The domain of a rational function is the set of all real numbers except for the value(s) of that make the denominator zero. The value(s) can be found as follows:

The domain is the set of all real numbers except - or .

Example Question #27 : How To Find The Domain Of A Function

Give the domain of the function

Possible Answers:

The set of all real numbers

Correct answer:

Explanation:

Since the radicand of a square root must be nonnegative, the domain of a radical function with a square root can be found by setting the radicand greater than or equal to 0:

This is the domain, which can also be stated as .

 

 

Example Question #121 : Algebraic Functions

Give the domain of the function

Possible Answers:

The set of all real numbers

Correct answer:

Explanation:

Since the radicand of a square root must be nonnegative, the domain of a radical function with a square root can be found by setting the radicand greater than or equal to 0:

[note the switch of symbol because of division by a negative number]

This is the domain, which can also be stated as .

Example Question #21 : How To Find The Domain Of A Function

Give the domain of the function

Possible Answers:

The set of all real numbers

Correct answer:

The set of all real numbers

Explanation:

The domain of a rational function is the set of all real numbers except for the value(s) of that make the denominator zero. The value(s) can be found as follows:

However, there is no real value of whose square is , so this statement has no solution. Therefore, there is no real value of which makes the denominator zero. The domain of is consequently the set of all real numbers.

Example Question #21 : How To Find The Domain Of A Function

Give the domain of the function

Possible Answers:

The set of all real numbers

Correct answer:

The set of all real numbers

Explanation:

is a polynomial function. The domain of any polynomial function is the set of all real numbers, making that the correct choice.

Learning Tools by Varsity Tutors