If the range of \( f(x) \) is given by \( (-3,1] \), what is the range of \( |f(x)| \) ? The range of \( |f(x)| \) is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

To find the range of \( |f(x)| \), we need to consider the effect of the absolute value function on the range of \( f(x) \). Given that the range of \( f(x) \) is \( (-3,1] \), this means that \( f(x) \) can take any value between -3 (not including -3) and 1 (including 1). The absolute value function, \( |x| \), always returns a non-negative value. Therefore, when we apply the absolute value to \( f(x) \), any negative values in the range of \( f(x) \) will be made positive, and the value 1 will remain the same since it's already non-negative. So, the range of \( |f(x)| \) will be all non-negative values that are less than or equal to the maximum value of \( f(x) \), which is 1. The minimum value of \( |f(x)| \) will be 0, since the absolute value of any negative number is positive, and the absolute value of 0 is 0. Therefore, the range of \( |f(x)| \) is \( [0,1] \). In interval notation, the range of \( |f(x)| \) is: \[ [0,1] \]