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

Problem

y=−1/2*cos(x)

Solution

1. Identify the parent function and its range. The basic cosine function y=cos(x) oscillates between −1 and 1

Range of *cos(x):−1≤cos(x)≤1

2. Apply the vertical scaling factor. The function is multiplied by −1/2 which affects the amplitude and reflects the graph across the xaxis.

−1≤cos(x)≤1

3. Multiply all parts of the inequality by −1/2 Remember that multiplying by a negative number reverses the inequality signs.

−1⋅(−1/2)≥−1/2*cos(x)≥1⋅(−1/2)

4. Simplify the values to find the minimum and maximum of the range.

1/2≥y≥−1/2

5. Rewrite the range in standard interval notation or as a simplified inequality.

−1/2≤y≤1/2

Final Answer

Range: *[−1/2,1/2]

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