Graph y=2-1/2 square root of x

$y = 2 - \frac{1}{2} \sqrt{x}$

Find the domain for $y = 2 - \frac{1}{2} \cdot \sqrt{x}$ so that a list of $x$ values can be picked to find a list of points, which will help graphing the radical.

Set the radicand in $\sqrt{x}$ greater than or equal to $0$ to find where the expression is defined.

$x \geq 0$

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

To find the radical expression end point, substitute the $x$ value $0$ , which is the least value in the domain, into $f (x) = 2 - \frac{\sqrt{x}}{2}$ .

Replace the variable $x$ with $0$ in the expression.

$f (0) = 2 - \frac{\sqrt{0}}{2}$

Simplify the result.

Simplify each term.

Simplify the numerator.

Rewrite $0$ as $0^{2}$ .

$f (0) = 2 - \frac{\sqrt{0^{2}}}{2}$

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

$f (0) = 2 - \frac{0}{2}$

Divide $0$ by $2$ .

$f (0) = 2 - 0$

Multiply $- 1$ by $0$ .

$f (0) = 2 + 0$

Add $2$ and $0$ .

$f (0) = 2$

The final answer is $2$ .

$2$

The radical expression end point is $(0, 2)$ .

$(0, 2)$

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

Substitute the $x$ value $1$ into $f (x) = 2 - \frac{\sqrt{x}}{2}$ . In this case, the point is $(1, \frac{3}{2})$ .

Replace the variable $x$ with $1$ in the expression.

$f (1) = 2 - \frac{\sqrt{1}}{2}$

Simplify the result.

Any root of $1$ is $1$ .

$f (1) = 2 - \frac{1}{2}$

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$f (1) = 2 \cdot \frac{2}{2} - \frac{1}{2}$

Combine $2$ and $\frac{2}{2}$ .

$f (1) = \frac{2 \cdot 2}{2} - \frac{1}{2}$

Combine the numerators over the common denominator.

$f (1) = \frac{2 \cdot 2 - 1}{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

$f (1) = \frac{4 - 1}{2}$

Subtract $1$ from $4$ .

$f (1) = \frac{3}{2}$

The final answer is $\frac{3}{2}$ .

$y = \frac{3}{2}$

Substitute the $x$ value $2$ into $f (x) = 2 - \frac{\sqrt{x}}{2}$ . In this case, the point is $(2, 2 - \frac{\sqrt{2}}{2})$ .

Replace the variable $x$ with $2$ in the expression.

$f (2) = 2 - \frac{\sqrt{2}}{2}$

The final answer is $2 - \frac{\sqrt{2}}{2}$ .

$y = 2 - \frac{\sqrt{2}}{2}$

The square root can be graphed using the points around the vertex $(0, 2), (1, 1.5), (2, 1.29)$

$\begin{array}{c} x & y \\ 0 & 2 \\ 1 & 1.5 \\ 2 & 1.29 \end{array}$

Graph y=2-1/2 square root of x

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