Question

Fill in the information about the absolute value functions below.

Answer 1

EXPLANATION:

We are given the absolute value functions below;

$\begin{gathered} y=3|x| \\ y=-\frac{3}{4}|x| \\ y=-\frac{1}{2}|x| \\ y=-1|x| \end{gathered}$

Note that for this function, we have a v-shaped graph, since the values of the output is always positive (absolute value) and the vertex is at (0, 0). Also, if the value of a in the function;

$y=a|x|$

is positive, the graph opens upwards, and if the value of a is negative;

$y=-a|x|$

then it opens downwards.

Therefore,

ANSWER;

$\begin{gathered} y=3|x|\text{ Opens upwards} \\ y=-\frac{3}{4}|x|\text{ Opens downwards} \\ y=-\frac{1}{2}|x|\text{ Opens downwards} \\ y=-1|x|\text{ Opens downwards} \end{gathered}$$\begin{gathered} The\text{ equation with the narrowest graph;} \\ y=3|x| \end{gathered}$$\begin{gathered} The\text{ equation with the widest graph;} \\ y=-\frac{1}{2}|x| \end{gathered}$