Every real number has a real cube root, so the radical does not restrict the domain of. The denominator of the expression does restrict the domain, however, in that it cannot be equal to 0. This happens only if:

or, equivalently,. Therefore, 1000 is the only real number not in the domain of.

The expression under the radical is defined for all real values ofsince the index of the radical is 3.

Since the expression under the radical must be greater than or equal to zero, hence when, the. Thereafter theis an increasing function.

A relation is a function if and only if no-coordinate is paired with more than one-coordinate. We test each of these four values ofto see if this happens.

:

The points become:

Since-coordinate 1 is paired with two-coordinates, 2 and 9, the relation is not a function.

:

The points become:

Since-coordinate 3 is paired with two-coordinates, 0 and 9, the relation is not a function.

:

The points become:

Since-coordinates 3 and 5 are each paired with two different-coordinates, the relation is not a function.

:

The points become:

Since each-coordinate is paired with one and only one-coordinate, the relation is a function.is the correct choice.

Finding the domain is like finding out what possiblevalues you can plug in without getting an error message on your calculator. We are given the function:

To find the domain, first, know that you can't take the square root of a negative number. It turns out that the minimum number you can take the square root of is zero. Any number above zero, everything is good. Therefore,can equal 0 or above. This is written as an inequality as:

Solve forby subtracting 1 on both sides

So that's our domain!

The domain is the set of possible value for thevariable. We can find the impossible values ofby setting the denominator of the fractional function equal to zero, as this would yield an impossible equation.

Now we can solve for.

There is no real value ofthat will fit this equation; any real value squared will be a positive number.

The radicand is always positive, andis defined for all real values of. This makes the domain ofthe set of all real numbers.

The domain is the set of x-values that make the function defined.

This function is defined everywhere except at, since division by zero is undefined.

The domain of a rational function is the set of all values offor which the denominator isnotequal to 0, so we set the denominator to 0 and solve for.

这是一个二次函数,所以我们的因素the expression as, replacing the question marks with two numbers whose product is 9 and whose sum is. These numbers are, so

becomes

,

or.

This means that, or.

Therefore, 3 is the only number excluded from the domain.

The domain of a rational function is the set of all values offor which the denominator isnotequal to 0 (the value of the numerator is irrelevant), so we set the denominator to 0 and solve forto find the excluded values.

这是一个二次函数,所以我们的因素the expression as, replacing the question marks with two numbers whose product is 8 and whose sum is. These numbers are, so

becomes

So either

, in which case,

or, in which case.

Therefore, 2 and 4 are the only numbers excluded from the domain.