Finding Real Number Restrictions (2.6.2)

Question 1

• The denominator can never have a value of zero. That stipulation restricts the domain of the variable to exclude any values that yield a value of zero for the denominator.

Answer 1

• The denominator can never have a value of zero. That stipulation restricts the domain of the variable to exclude any values that yield a value of zero for the denominator.

Question 2

• The domain of the variable is the set of all real numbers that the variable can use.

Answer 2

• The domain of the variable is the set of all real numbers that the variable can use.

Question 3

• To find any value of the variable that makes the denominator equal zero, set the denominator equal to zero and solve that equation. This value(s) must be excluded from the domain of the variable.

Answer 3

• To find any value of the variable that makes the denominator equal zero, set the denominator equal to zero and solve that equation. This value(s) must be excluded from the domain of the variable.

Question 4

What is the Domain?

Answer 4

The Domain is every place where the denominator is not zero.

Question 5

To find the domain of an expression, first factor the
denominator.

Next set each factor equal to zero to see what values of x must be eliminated from the domain.

If an equation is too complex to be easily factored, use the quadratic formula. It will show you every number that must be excluded.

Answer 5

To find the domain of an expression, first factor the
denominator.

Next set each factor equal to zero to see what values of x must be eliminated from the domain.

If an equation is too complex to be easily factored, use the quadratic formula. It will show you every number that must be excluded.

Question 6

To find the domain for this expression, factor the
denominator.

Then set the factor(s) equal to zero and solve for x.

This solution is the one real number that must be excluded from the domain of x.

Answer 6

To find the domain for this expression, factor the
denominator.

Then set the factor(s) equal to zero and solve for x.

This solution is the one real number that must be excluded from the domain of x.

Question 7

This example shows you a different result.

This denominator can equal zero only when x has the value of an imaginary number.

Therefore, no real numbers are excluded and the domain is all real numbers.

Answer 7

This example shows you a different result.

This denominator can equal zero only when x has the value of an imaginary number.

Therefore, no real numbers are excluded and the domain is all real numbers.