Find the magnitude of the trig term <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn></mstyle></math> by taking the absolute value of the coefficient.

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

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

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

Subtract <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The range is <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn><mo>≤</mo><mi>y</mi><mo>≤</mo><mn>0</mn></mstyle></math> .

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