английский грузинский русский \( y=|x-3| \) The smallest and largest values of the function \( [3 ; 4] \) in the interval, therefore, there are:

To find the smallest and largest values of the function \( y = |x - 3| \) in the interval \([3, 4]\), we can evaluate the function at the endpoints of the interval and check for any critical points within the interval. 1. **Evaluate at the endpoints:** - At \( x = 3 \): \[ y = |3 - 3| = |0| = 0 \] - At \( x = 4 \): \[ y = |4 - 3| = |1| = 1 \] 2. **Check for critical points:** The function \( y = |x - 3| \) is piecewise defined: - For \( x < 3 \), \( y = 3 - x \) - For \( x \geq 3 \), \( y = x - 3 \) In the interval \([3, 4]\), the function is defined as \( y = x - 3 \). This is a linear function, which is increasing in this interval. 3. **Determine the smallest and largest values:** - The smallest value occurs at \( x = 3 \): \( y = 0 \) - The largest value occurs at \( x = 4 \): \( y = 1 \) Thus, the smallest value of the function in the interval \([3, 4]\) is \( 0 \), and the largest value is \( 1 \). **Final Answer:** - Smallest value: \( 0 \) - Largest value: \( 1 \)