f(x) = sin x
f'(x) = cos x
1. What is the domain of f(x)?
The domain of f(x) is all real numbers since we can take the sine of any real number.
2. What is the range of f(x)?
The range of f(x) is [-1, 1]. This is because the sine function oscillates between -1 and 1 as x increases or decreases.
3. Is f(x) an even, odd, or neither function?
The function f(x) is an odd function. This is because f(-x) = -sin x = -f(x), meaning that the function is symmetric about the origin.
4. What are the x and y intercepts of the graph of f(x)?
The x-intercepts are at x = nπ for any integer n, since sin(nπ) = 0 for any integer n. There are no y-intercepts for the graph of sin x since the function oscillates between -1 and 1 and never crosses the y-axis.
5. What is the period of the graph of f(x)?
The period of the graph of sin x is 2π. This means that the graph repeats itself every 2π units.
6. What is the amplitude of the graph of f(x)?
The amplitude of the graph of sin x is 1. The amplitude refers to the distance from the maximum or minimum value of the function to the horizontal axis.
7. What are the maximum and minimum values of the graph of f(x)?
The maximum value of the graph of sin x is 1 and the minimum value is -1. This occurs at every multiple of π/2 radians.
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