Graph y=3- square root of 1-x

$y = 3 - \sqrt{1 - x}$

Reorder $1$ and $- x$ .

$y = 3 - \sqrt{- x + 1}$

Find the domain for $y = 3 - \sqrt{1 - x}$ 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 $\sqrt{- x + 1}$ greater than or equal to $0$ to find where the expression is defined.

$- x + 1 \geq 0$

Solve for $x$ .

Subtract $1$ from both sides of the inequality.

$- x \geq - 1$

Divide each term in $- x \geq - 1$ by $- 1$ and simplify.

Divide each term in $- x \geq - 1$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{- 1}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{- 1}{- 1}$

Divide $x$ by $1$ .

$x \leq \frac{- 1}{- 1}$

Simplify the right side.

Divide $- 1$ by $- 1$ .

$x \leq 1$

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

Interval Notation:

$(- \infty, 1]$

Set-Builder Notation:

${x | x \leq 1}$

Interval Notation:

$(- \infty, 1]$

Set-Builder Notation:

${x | x \leq 1}$

To find the radical expression end point, substitute the $x$ value $1$ , which is the least value in the domain, into $f (x) = 3 - \sqrt{- x + 1}$ .

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

$f (1) = 3 - \sqrt{- (1) + 1}$

Simplify the result.

Simplify each term.

Multiply $- 1$ by $1$ .

$f (1) = 3 - \sqrt{- 1 + 1}$

Add $- 1$ and $1$ .

$f (1) = 3 - \sqrt{0}$

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

$f (1) = 3 - \sqrt{0^{2}}$

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

$f (1) = 3 - 0$

Multiply $- 1$ by $0$ .

$f (1) = 3 + 0$

Add $3$ and $0$ .

$f (1) = 3$

The final answer is $3$ .

$3$

The radical expression end point is $(1, 3)$ .

$(1, 3)$

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

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

$f (- 1) = 3 - \sqrt{- (- 1) + 1}$

Simplify the result.

Simplify each term.

Multiply $- 1$ by $- 1$ .

$f (- 1) = 3 - \sqrt{1 + 1}$

Add $1$ and $1$ .

$f (- 1) = 3 - \sqrt{2}$

The final answer is $3 - \sqrt{2}$ .

$y = 3 - \sqrt{2}$

Substitute the $x$ value $0$ into $f (x) = 3 - \sqrt{- x + 1}$ . In this case, the point is $(0, 2)$ .

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

$f (0) = 3 - \sqrt{- (0) + 1}$

Simplify the result.

Simplify each term.

Multiply $- 1$ by $0$ .

$f (0) = 3 - \sqrt{0 + 1}$

Add $0$ and $1$ .

$f (0) = 3 - \sqrt{1}$

Any root of $1$ is $1$ .

$f (0) = 3 - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$f (0) = 3 - 1$

Subtract $1$ from $3$ .

$f (0) = 2$

The final answer is $2$ .

$y = 2$

The square root can be graphed using the points around the vertex $(1, 3), (- 1, 1.59), (0, 2)$

$\begin{array}{c} x & y \\ - 1 & 1.59 \\ 0 & 2 \\ 1 & 3 \end{array}$

Graph y=3- square root of 1-x

Related Questions

Support LCMGCF.com by disabling your adblocker.