Graph f(x)=|2sin(1/2)-3|-1

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Trigonometry

$f (x) = | 2 \sin (\frac{1}{2}) - 3 | - 1$

Find the absolute value vertex. In this case, the vertex for $y = 1.04114892$ is $(0, 1.04114892)$ .

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To find the $x$ coordinate of the vertex, set the inside of the absolute value equal to $0$ . In this case, $= 0$ .

$= 0$

Since there is no variable to replace, the result is $1.04114892$ .

$y = 1.04114892$

The absolute value vertex is $(0, 1.04114892)$ .

$(0, 1.04114892)$

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

For each $x$ value, there is one $y$ value. Select few $x$ values from the domain. It would be more useful to select the values so that they are around the $x$ value of the absolute value vertex.

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Substitute the $x$ value $- 2$ into $y = 1.04114892$ . In this case, the point is $(- 2, 1.04114892)$ .

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Replace the variable $y$ with $- 2$ in the expression.

$f (- 2) = 1.04114892$

The final answer is $1.04114892$ .

$y = 1.04114892$

The absolute value can be graphed using the points around the vertex $(0, 1.04114892), (- 2, 1.04), (- 1, 1.04), (1, 1.04), (2, 1.04)$

$\begin{array}{c} x & y \\ - 2 & 1.04 \\ - 1 & 1.04 \\ 0 & 1.041 \\ 1 & 1.04 \\ 2 & 1.04 \end{array}$

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