Question

Complete the description of the piecewise function graphed below.

-6 -5
4
2
H+
-2-7
{
f(x) = {
+
-2
-3
-4
-S
3
Question Help:
1 2
{ -X
Vide
if -6 ≤x≤-1
if -1 < x < 2
if 2

Answer 1

The complete description of the piecewise function is:

f(x) = (5/2)x + (13/2) if {-6 ≤ x ≤ -1},

f(x) = 3 if {-1 < x ≤ 2},

f(x) = -x if {2 < x ≤ 6},

To complete the description of the piecewise function graphed below:

{-6 ≤ x ≤ -1}: In this segment, the function is a linear equation with a positive slope of 5/2 and a y-intercept of 13/2. This means that as x increases, the value of f(x) also increases, but at a constant rate of 5/2.

{-1 < x ≤ 2}: In this segment, the function becomes a horizontal line at a constant value of f(x) = 3. This means that regardless of the change in x, f(x) remains constant.

{2 < x ≤ 6}: In this segment, the function becomes a linear equation with a negative slope of -1. This means that as x increases, the value of f(x) decreases at a constant rate of -1.

Therefore, the complete description of the piecewise function is:

if {-6 ≤ x ≤ -1}, f(x) = (5/2)x + (13/2)

if {-1 < x ≤ 2}, f(x) = 3

if {2 < x ≤ 6}, f(x) = -x