Satisfying the Domain of a Function (3.8.3)

Question 1

• The domain is the set of all real number values that can be used for x

Answer 1

• The domain is the set of all real number values that can be used for x

Question 2

• R is the notational symbol for the set of all real numbers.

Answer 2

• R is the notational symbol for the set of all real numbers.

Question 3

• R / {a1, a2, …} is the notation for a domain or range of all real numbers except certain ones.

Answer 3

• R / {a1, a2, …} is the notation for a domain or range of all real numbers except certain ones.

Question 4

In this example, all real numbers can be used for x because
any number can be squared and then subtracted.
In this problem if you try using a value larger than ¾, you
will have a negative number under the square root sign. The
domain does not allow you to include anything like that.
It is OK to create 0 under the square root sign because the
square root of 0 is 0. So, you are restricted in your domain
for this function to numbers that are less than or equal to +3/4,
as shown.
This example shows values eliminated from the domain
because they create denominators that equal 0.
Notice these excluded values for x are discovered by setting
the denominator equal to 0 and solving for x by factoring.
Here is one notation for the domain when specific values are
excluded.
In this example, first factor the denominator and notice you
can cancel one factor with itself in the numerator.
Remember: Even if an expression is factored out, any value
for x that would make the canceled expression equal 0 must
still be excluded.
Any activity performed with a rational expression must clearly
state what values are to be excluded.

Answer 4

In this example, all real numbers can be used for x because
any number can be squared and then subtracted.
In this problem if you try using a value larger than ¾, you
will have a negative number under the square root sign. The
domain does not allow you to include anything like that.
It is OK to create 0 under the square root sign because the
square root of 0 is 0. So, you are restricted in your domain
for this function to numbers that are less than or equal to +3/4,
as shown.
This example shows values eliminated from the domain
because they create denominators that equal 0.
Notice these excluded values for x are discovered by setting
the denominator equal to 0 and solving for x by factoring.
Here is one notation for the domain when specific values are
excluded.
In this example, first factor the denominator and notice you
can cancel one factor with itself in the numerator.
Remember: Even if an expression is factored out, any value
for x that would make the canceled expression equal 0 must
still be excluded.
Any activity performed with a rational expression must clearly
state what values are to be excluded.