# Graph f(x)=1/2 square root of x-1

Find the domain for so that a list of values can be picked to find a list of points, which will help graphing the radical.

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Set the radicand in greater than or equal to to find where the expression is defined.

The domain is all values of that make the expression defined.

Interval Notation:

Set-Builder Notation:

Interval Notation:

Set-Builder Notation:

To find the radical expression end point, substitute the value , which is the least value in the domain, into .

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Replace the variable with in the expression.

Simplify the result.

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Simplify each term.

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Simplify the numerator.

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Rewrite as .

Pull terms out from under the radical, assuming positive real numbers.

Divide by .

Subtract from .

The final answer is .

The radical expression end point is .

Select a few values from the domain. It would be more useful to select the values so that they are next to the value of the radical expression end point.

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Substitute the value into . In this case, the point is .

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Replace the variable with in the expression.

Simplify the result.

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Any root of is .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

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Multiply by .

Subtract from .

Move the negative in front of the fraction.

The final answer is .

Substitute the value into . In this case, the point is .

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Replace the variable with in the expression.

The final answer is .

The square root can be graphed using the points around the vertex

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