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.
oa ob oc od

Explanation:

Step1: Recall the property of $y = k|x|$ graph

The graph of $y = k|x|$ is a V - shaped graph. If $k>0$, the graph opens upwards; if $k < 0$, the graph opens downwards. Given $A,B,C$ have upward - opening graphs, so $A>0,B>0,C>0$, and $D$ has a downward - opening graph, so $D<0$.

Step2: Analyze the steepness of the graph

The larger the absolute value of the coefficient $k$ in $y = k|x|$, the steeper the graph. The closer the absolute value of $k$ is to 0, the flatter the graph. Among the four graphs, the graph of $y = B|x|$ is the flattest. So the coefficient closest to 0 is $B$.

Answer:

A. positive
B. positive
C. positive
D. negative
(b) B