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 { }.
(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 when \( f(x) = 0 \)

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). From the given graph, we observe that the graph of the rational function does not intersect the \( x \)-axis at any point. This means there are no \( x \)-values for which \( f(x)=0 \).

Answer:

C. The solution set is the empty set.