Final answer:
The functions that have the given properties are the sine and cosine functions. The sine function is odd, with x-intercepts at integer multiples of pi and a minimum value of -1 at x=3pi/2. The cosine function is also odd, with x-intercepts at odd multiples of pi/2 and a minimum value of -1 at x=pi.
Step-by-step explanation:
The functions that have the given properties are the sine and cosine functions.
- The sine function: The sine function is odd, which means that it satisfies the property of being an odd function. The x-intercepts of the sine function are at integer multiples of pi, and the minimum value is -1 at x=3pi/2.
- The cosine function: The cosine function is also an odd function. The x-intercepts of the cosine function are at odd multiples of pi/2, and the minimum value is -1 at x=pi.
Therefore, the functions that satisfy all the given properties are the sine and cosine functions.