Question

use the graph of the function f shown to the right to answer parts (a)-(n).
$f(0)=-1$
(c) is f(8) positive or negative?
positive
negative
(d) is f(-8) positive or negative?
positive
negative
(e) for what value(s) of x is f(x)=0?
$x=-24,-4,16$
(use a comma to separate answers as needed.)
(f) for what values of x is f(x) > 0?
(type a compound inequality. use a comma to separate answers as needed.)

Explanation:

Step1: Identify f(x)>0 regions

Look for where the graph is above the x-axis (y>0).

1. First interval: Between $x=-24$ and $x=-4$, the graph is above the x-axis.
2. Second interval: Between $x=16$ and $x=24$, the graph is above the x-axis.

Step2: Write compound inequalities

Express the intervals using inequality notation:

• For the first region: $-24 < x < -4$
• For the second region: $16 < x < 24$

Answer:

$-24 < x < -4, 16 < x < 24$