jmc

Question

If f(x) is a function defined only for 0 x 1, and f(x) = ax+b for constants a and b where a < 0, then what is the range of f in terms of a and b? Express your answer in interval notation.

Accepted Answer

The function f(x) = ax + b is linear, so as x varies over the interval 0 x 1, f(x) = ax + b takes on all values between b and a + b (inclusive). Furthermore, a < 0, so a + b < b. Hence, the range of f(x) is [a +b, b].