Question

For each function choose whether it’s graph opens upward or downward. Choose the equation with the whitest graph. Choose the equation with the narrowest graph.

Answer 1

To understand how to solve the question let us draw the given functions

`\begin{gathered} y=(1)/(2)\lvert x\rvert \\ y=2\lvert x\rvert \\ y=-(1)/(3)\lvert x\rvert \\ y=-1\lvert x\rvert \end{gathered}`

The red graph represents the 1st function

The blue graph represents the 2nd function

The green graph represents the 3rd function

The purple graph represents the 4th function

1st and 2nd function opened upward

3rd and 4th functions opened downward

The widest graph is the green graph, (nearest to the x-axis)

Its equation is

`y=-(1)/(3)\lvert x\rvert`

The narrowest graph is the blue graph, (furthest from the x-axis)

Its equation is

`y=2\lvert x\rvert`