If $f(x)$ is a function defined only for $0 \le x \le 1$, 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.
f(x) is defined only for 0 ≤ x ≤ 1 , and f(x) = ax + b for constants a and b where a < 0 .
Since a is negative, the smallest possible value for f(x) will be when x = 1 .
f(1) = a(1) + b = a + b
Then, the largest possible value for f(x) will be when x = 0 .
f(0) = a(0) + b = b
The smallest possible value for f(x) is a + b , and the largest possible value for f(x) is b .
So......the range for f(x) is [ a + b , b ] .
f(x) is defined only for 0 ≤ x ≤ 1 , and f(x) = ax + b for constants a and b where a < 0 .
Since a is negative, the smallest possible value for f(x) will be when x = 1 .
f(1) = a(1) + b = a + b
Then, the largest possible value for f(x) will be when x = 0 .
f(0) = a(0) + b = b
The smallest possible value for f(x) is a + b , and the largest possible value for f(x) is b .
So......the range for f(x) is [ a + b , b ] .