The range of the parent sine function is all real numbers between __________ and __________ (fill in the smaller value first).
Answer & Analysis
Analysis
Question Analysis
This question involves the output values (range) of the parent sine function. The main focus is on identifying the minimum and maximum y-values that can produce, with no transformations applied.
Key Concept Explanation
The range of a function is the set of all possible output (y-) values. For the parent sine function , the graph oscillates (moves up and down) between two fixed values: it never rises above 1 or falls below -1. These are the "peak" (maximum) and "trough" (minimum) of the sine wave.
Step-by-step Solution
1. Recall the definition of range: all possible y-values of the function.
2. Identify the maximum y-value of : The graph reaches its highest point at (e.g., at , , etc.).
3. Identify the minimum y-value of
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