Graph f(x)=-1/5 square root of x-1-4

$f (x) = - \frac{1}{5} \sqrt{x - 1} - 4$

Find the domain for $y = - \frac{1}{5} \cdot \sqrt{x - 1} - 4$ 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.

$x - 1 \geq 0$

Add $1$ to both sides of the inequality.

$x \geq 1$

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

Interval Notation:

$[1, \infty)$

Set-Builder Notation:

${x | x \geq 1}$

Interval Notation:

$[1, \infty)$

Set-Builder Notation:

${x | x \geq 1}$

To find the radical expression end point, substitute the $x$ value $1$ , which is the least value in the domain, into $f (x) = - \frac{\sqrt{x - 1} + 20}{5}$ .

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

$f (1) = - \frac{\sqrt{(1) - 1} + 20}{5}$

Simplify the result.

Simplify the numerator.

Subtract $1$ from $1$ .

$f (1) = - \frac{\sqrt{0} + 20}{5}$

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

$f (1) = - \frac{\sqrt{0^{2}} + 20}{5}$

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

$f (1) = - \frac{0 + 20}{5}$

Add $0$ and $20$ .

$f (1) = - \frac{20}{5}$

Simplify the expression.

Divide $20$ by $5$ .

$f (1) = - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$f (1) = - 4$

The final answer is $- 4$ .

$- 4$

The radical expression end point is $(1, - 4)$ .

$(1, - 4)$

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 $2$ into $f (x) = - \frac{\sqrt{x - 1} + 20}{5}$ . In this case, the point is $(2, - \frac{21}{5})$ .

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

$f (2) = - \frac{\sqrt{(2) - 1} + 20}{5}$

Simplify the result.

Simplify the numerator.

Subtract $1$ from $2$ .

$f (2) = - \frac{\sqrt{1} + 20}{5}$

Any root of $1$ is $1$ .

$f (2) = - \frac{1 + 20}{5}$

Add $1$ and $20$ .

$f (2) = - \frac{21}{5}$

The final answer is $- \frac{21}{5}$ .

$y = - \frac{21}{5}$

Substitute the $x$ value $3$ into $f (x) = - \frac{\sqrt{x - 1} + 20}{5}$ . In this case, the point is $(3, - \frac{\sqrt{2} + 20}{5})$ .

Replace the variable $x$ with $3$ in the expression.

$f (3) = - \frac{\sqrt{(3) - 1} + 20}{5}$

Simplify the result.

Subtract $1$ from $3$ .

$f (3) = - \frac{\sqrt{2} + 20}{5}$

The final answer is $- \frac{\sqrt{2} + 20}{5}$ .

$y = - \frac{\sqrt{2} + 20}{5}$

The square root can be graphed using the points around the vertex $(1, - 4), (2, - 4.2), (3, - 4.28)$

$\begin{array}{c} x & y \\ 1 & - 4 \\ 2 & - 4.2 \\ 3 & - 4.28 \end{array}$

Graph f(x)=-1/5 square root of x-1-4

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