Questions: Suppose that the function f is defined, for all real numbers as follows: f(x) = - 3x + 1 if x < -2 - x - 3 if x ≥ -2 Graph the function f. Then determine whether or not the

Suppose that the function f is defined, for all real numbers as follows:

f(x) =
- 3x + 1 if x < -2
- x - 3 if x ≥ -2

Graph the function f. Then determine whether or not the

Transcript text: Suppose that the function $f$ is defined, for all real num \[ f(x)=\left\{\begin{array}{cc} 3 x+1 & \text { if } x<-2 \\ x-3 & \text { if } x \geq-2 \end{array}\right. \] Graph the function $f$. Then determine whether or not th

Solution

Solution Steps

Step 1: Understand the Piecewise Function

The function $ f(x) $ is defined as: \[ f(x) = \begin{cases} 3x + 1 & \text{if } x < -2 \\ x - 3 & \text{if } x \geq -2 \end{cases} \]

Step 2: Graph the First Piece of the Function

For $ x < -2 $, the function is $ f(x) = 3x + 1 $. This is a linear function with a slope of 3 and a y-intercept of 1. Plot this line for values of $ x $ less than -2.

Step 3: Graph the Second Piece of the Function

For $ x \geq -2 $, the function is $ f(x) = x - 3 $. This is a linear function with a slope of 1 and a y-intercept of -3. Plot this line for values of $ x $ greater than or equal to -2.