Find the Range y=-4sin(x)

Problem

y=−4*sin(x)

Solution

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

Range of *sin(x):[−1,1]

2. Determine the inequality for the parent function. This can be expressed as:

−1≤sin(x)≤1

3. Apply the transformation by multiplying the entire inequality by the coefficient −4 Note that multiplying by a negative number reverses the inequality signs.

−4*(1)≤−4*sin(x)≤−4*(−1)

4. Simplify the resulting values to find the boundaries of the range.

−4≤−4*sin(x)≤4

5. Conclude that the output values y are contained within the interval from −4 to 4

Range:[−4,4]

Final Answer

Range of *y=−4*sin(x)=[−4,4]

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