Question

use the graph of the function f shown to answer parts (a)-(n).
(c) is f(2) positive or negative?
positive
negative
(d) is f(-3) positive or negative?
positive
negative
(e) for what value(s) of x is f(x)=0?
x = -6, -1,4
(use a comma to separate answers as needed.)
(f) for what values of x is f(x)>0?
-6<x<-1,4<x≤6
(type a compound inequality. use a comma to separate answers as needed.)
(g) what is the domain of f?
the domain of f is {x| -7≤x≤6}.
(type a compound inequality.)
(h) what is the range of f?
the range of f is {y|□}.
(type a compound inequality.)

Explanation:

Step1: Determine the range of \( y \) values

The range of a function is the set of all possible \( y \) - values.
Looking at the graph, the lowest \( y \) - value is \( y=-4 \) (at the point \((-7, - 4)\) and \((2,-4)\)) and the highest \( y \) - value is \( y = 6 \) (at the point \((-3,6)\)).

Answer:

The range of \( f \) is \(\{y|-4\leq y\leq6\}\)