Question

This is an Algebraic Piecewise function question:I understand how to find the slope and y-intercept of the top and bottom solid lines, but am unsure what to do with the third line with the open points. Also I would like to express it as a function: f(x) { if

Answer 1

This piecewise function is divided in three sections.

You've already calculated the two segments for x less or equal then -2 and for x bigger or equal then 2.

The missing segment is the one at the interval -2 < x < 2.

A line equation is written as

`y=mx+b`

The 'm' is the slope of the function and 'b' is the y-intercept.

Since the middle segment cuts the y-axis at the value -2, this is our 'b' value.

The value of the middle segment decreases, which also means the slope is negative.

Analyzing the options we have, the middle segment is

[tex]y=-\frac{x}{3}-2,if-2