Find the Range y=cos(2x)-1

$y = \cos (2 x) - 1$

Find the magnitude of the trig term $\cos (2 x) - 1$ by taking the absolute value of the coefficient.

$1$

Find the lower bound of the range.

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The lower bound of the range for cosine is found by substituting the negative magnitude of the coefficient into the equation.

$y = - 1 - 1$

Subtract $1$ from $- 1$ .

$y = - 2$

Find the upper bound of the range.

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The upper bound of the range for cosine is found by substituting the positive magnitude of the coefficient into the equation.

$y = 1 - 1$

Subtract $1$ from $1$ .

$y = 0$

The range is $- 2 \leq y \leq 0$ .

Interval Notation:

$[- 2, 0]$

Set-Builder Notation:

${y | - 2 \leq y \leq 0}$

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