Question

the graph of a rational function ( y = f(x) ) is given. use the graph to give the solution set of the following.
(a) ( f(x) = 0 )
(b) ( f(x) < 0 )
(c) ( f(x) > 0 )
do not use a calculator.
(a) what is the solution set of ( f(x) = 0 )?
a. the solution set is (\boxed{}) (type an integer or a decimal. use a comma to separate answers as needed.)
b. the solution set is the set of all real numbers.
c. the solution set is the empty set.

Explanation:

Step1: Analyze the graph of \( f(x) \)

To find the solution set of \( f(x) = 0 \), we look for the \( x \)-values where the graph of \( y = f(x) \) intersects the \( x \)-axis (since \( y = 0 \) on the \( x \)-axis).

Looking at the given graph, we observe that the graph of the rational function does not intersect the \( x \)-axis at any point. This is because the graph either approaches asymptotes or is above/below the \( x \)-axis but never actually crosses or touches the \( x \)-axis (where \( y = 0 \)).

Step2: Determine the solution set

Since there are no \( x \)-values for which \( f(x) = 0 \), the solution set is the empty set. So the correct option is C.

Answer:

C. The solution set is the empty set.