Question

use the graph of the function f to solve the inequality.
(a) ( f(x)<0 )
(b) ( f(x) geq 0 )

Explanation:

Step1: Analyze \( f(x)<0 \)

We need to find the \( x - \)values for which the graph of \( y = f(x) \) lies below the \( x - \)axis (\( y = 0 \)).
Looking at the graph, the function \( y=f(x) \) is below the \( x - \)axis when \( x\in(-3,0)\cup(1,\infty) \).

Step2: Analyze \( f(x)\geq0 \)

We need to find the \( x - \)values for which the graph of \( y = f(x) \) lies on or above the \( x - \)axis (\( y = 0 \)).
Looking at the graph, the function \( y = f(x) \) is on or above the \( x - \)axis when \( x\in(-\infty,-3)\cup[0,1] \).

Answer:

(a) \( x\in(-3,0)\cup(1,\infty) \)
(b) \( x\in(-\infty,-3)\cup[0,1] \)