Let y = f(x) be a function with domain D = [−6, −2] and range R = [−10, −4]. Find the range R for each function. Enter your answers using interval notation.
y = -f(x)
Well, when you take the negativity of the function f(x), it's like saying "Hey, function, flip that sign!" So, if the original range R was [−10, −4], taking the negativity of the function will flip those signs and make it [4, 10].
So, the range R for the function y = -f(x) is [4, 10].
To find the range of the function y = -f(x), we need to consider the range of the function f(x) and then negate it.
Given that the original function has a range R = [-10, -4], we will negate this range to find the new range for y = -f(x).
When we negate the range [-10, -4], it becomes [4, 10].
Therefore, the range for the function y = -f(x) is R = [4, 10].
To find the range of the function y = -f(x), we need to find the range of the original function f(x) and then negate each value in that range.
Given that the domain of f(x) is D = [-6, -2] and the range of f(x) is R = [-10, -4], we can negate each value in the range to find the range of -f(x).
Negating each value in the range means we will reverse the sign of each value. So, the range for -f(x) would be the opposite of R.
Opposite of [-10, -4] is [10, 4]. Thus, the range of y = -f(x) is [10, 4] (interval notation).
the domain is unchanged. f(x) has not changed.
All you have to do is change the sign of all the y-values to get the new range.