Find the largest and smallest value of the linear function 3x + y-2 = 0. On the segment (-1; 1).

1. Let’s express the variable y in terms of x:

3x + y – 2 = 0;

y = -3x + 2.

2. A linear function with a negative first coefficient is a decreasing function on the entire set of real numbers, therefore, takes its smallest value at the right end of a given segment [-1; 1], and the largest value is at the left end of the same segment:

y (min) = y (1) = -3 * 1 + 2 = -3 + 2 = -1;
y (max) = y (-1) = -3 * (-1) + 2 = 3 + 2 = 5.
Answer:

a) the smallest value of the function is -1;
b) the highest value of the function 5.