Question

(a) for each coefficient, choose whether it is positive or negative. a: positive b: positive c: positive d: negative (b) choose the coefficient closest to 0. a b c d (c) choose the coefficient with the least value. a b c d

Explanation:

Step1: Analyze absolute - value function behavior

The general form of an absolute - value function is $y = k|x|$. When $k>0$, the graph opens upwards, and when $k < 0$, the graph opens downwards. Graphs of $y = A|x|$, $y = B|x|$, $y = C|x|$ open upwards, so $A>0$, $B>0$, $C>0$. The graph of $y = D|x|$ opens downwards, so $D<0$.

Step2: Determine coefficient closest to 0

The closer the coefficient of $|x|$ is to 0, the flatter the graph. The graph of $y = B|x|$ is the flattest among the positive - coefficient graphs, so $B$ is closest to 0.

Step3: Find coefficient with least value

Since $D$ is negative and $A$, $B$, $C$ are positive, the least value among $A$, $B$, $C$, $D$ is $D$.

Answer:

(b) B
(c) D