Question

use the graph of the function f shown to answer parts (a)-(n).
(a) find f(-7) and f(-3).
f(-7)=
f(-3)=
(b) find f(6) and f(0).
f(6)=
f(0)=
(c) is f(2) positive or negative?
positive
negative
(d) is f(-2) positive or negative?
negative
positive
(e) for what value(s) of x is f(x)=0?
x=
(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.)
(g) what is the domain of f?
the domain of f is {x|
(type a compound inequality.)

Explanation:

Step1: Find \( f(-7) \) and \( f(-3) \)

For \( f(-7) \), when \( x = -7 \), from the graph, the \( y - \)value (since \( y=f(x) \)) is \( - 8 \). So \( f(-7)=-8 \).
For \( f(-3) \), when \( x=-3 \), from the graph, the \( y - \)value is \( 12 \). So \( f(-3)=12 \).

Step2: Find \( f(6) \) and \( f(0) \)

For \( f(6) \), when \( x = 6 \), from the graph, the \( y - \)value is \( 8 \). So \( f(6)=8 \).
For \( f(0) \), when \( x = 0 \), from the graph, the \( y - \)value is \( - 4 \). So \( f(0)=-4 \).

Step3: Determine if \( f(2) \) is positive or negative

When \( x = 2 \), from the graph, the \( y - \)value ( \( y=f(2) \)) is below the \( x - \)axis. So \( f(2)\) is negative.

Step4: Determine if \( f(-2) \) is positive or negative

When \( x=-2 \), from the graph, the \( y - \)value ( \( y = f(-2)\)) is above the \( x - \)axis. So \( f(-2)\) is positive.

Step5: Find \( x \) such that \( f(x)=0 \)

The graph intersects the \( x - \)axis at \( x=-6,x = 1,x = 4 \). So \( x=-6,1,4 \).

Step6: Find \( x \) such that \( f(x)>0 \)

The graph is above the \( x - \)axis when \( -6\lt x\lt1 \) or \( 4\lt x\lt6 \).

Step7: Find the domain of \( f \)

The left - most \( x - \)value is \( x=-7 \) and the right - most \( x - \)value is \( x = 6 \). So the domain is \( -7\leq x\leq6 \).

Answer:

a. \( f(-7)=-8 \), \( f(-3)=12 \)
b. \( f(6)=8 \), \( f(0)=-4 \)
c. Negative
d. Positive
e. \( x=-6,1,4 \)
f. \( -6\lt x\lt1,4\lt x\lt6 \)
g. \( -7\leq x\leq6 \)