\( y=3|x|, \quad y=\frac{1}{3}|x|, \quad y=-\frac{1}{4}|x|, \quad y=-4|x| \) For each function, choose whether its graph opens upward or downward,

The graphs of the functions you provided are all based on the absolute value function, which produces V-shaped graphs. Functions of the form \( y = k|x| \) where \( k > 0 \) open upward, while those where \( k < 0 \) open downward. - For \( y = 3|x| \) and \( y = \frac{1}{3}|x| \) (both have \( k > 0 \)), these graphs open **upward**. - For \( y = -\frac{1}{4}|x| \) and \( y = -4|x| \) (both have \( k < 0 \)), these graphs open **downward**. So, summarizing: \( y = 3|x| \) and \( y = \frac{1}{3}|x| \) open upward, while \( y = -\frac{1}{4}|x| \) and \( y = -4|x| \) open downward!