Question

use the graph of the function f shown to answer parts (a)-(n)
(d) is f(-6) positive or negative?
negative
positive
(e) for what value(s) of x is f(x)=0?
x = -21,-5,13 (use a comma to separate answers as needed.)
(f) for what values of x is f(x)>0?
-21<x<-5,13<x<21 (type a compound - inequality. use a comma to separate answers as needed.)
(g) what is the domain of f?

Explanation:

Step1: Analyze f(-6)

Locate x = - 6 on the x - axis. Then, find the corresponding y - value on the graph of y = f(x). At x=-6, the y - value is above the x - axis, so f(-6)>0.

Step2: Find x for f(x)=0

Look for the x - values where the graph of y = f(x) intersects the x - axis. The intersection points occur at x=-21, x = - 5, and x = 13.

Step3: Find x for f(x)>0

Identify the intervals on the x - axis where the graph of y = f(x) is above the x - axis. The graph is above the x - axis when -21<x<-5 and 13<x<21.

Step4: Find the domain

The domain of a function is the set of all possible x - values for which the function is defined. Looking at the graph, the x - values range from -21 to 21. So the domain is -21≤x≤21.

Answer:

(d) Positive
(e) x=-21,-5,13
(f) -21<x<-5,13<x<21
(g) -21≤x≤21