Find the Range y=-3sec(x)

Problem

y=−3*sec(x)

Solution

1. Identify the parent function and its range. The parent function is sec(x) which is defined as 1/cos(x)

2. Recall the range of the basic secant function. Since |cos(x)|≤1 the reciprocal satisfies |sec(x)|≥1 This means the range of sec(x) is (−∞,−1]∪[1,∞)

3. Apply the vertical stretch and reflection. The function y=−3*sec(x) multiplies every output of the parent function by −3

4. Calculate the new boundaries. Multiplying the interval [1,∞) by −3 results in (−∞,−3] Multiplying the interval (−∞,−1] by −3 results in [3,∞)

5. Combine the intervals to determine the final range. The set of all possible yvalues is (−∞,−3]∪[3,∞)

Final Answer

Range:(−∞,−3]∪[3,∞)

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