Question

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Explanation:

Step1: Analyze the graph of the rational function

A rational function \( y = f(x) \) has a solution to \( f(x)=0 \) when the graph intersects the \( x \)-axis (i.e., when \( y = 0 \)). From the given graph, we observe that the graph of the rational function does not intersect the \( x \)-axis. This means there are no \( x \)-values for which \( f(x)=0 \).

Step2: Determine the solution set

Since there are no \( x \)-values that satisfy \( f(x) = 0 \), the solution set is the empty set. So we choose option B.

Answer:

B. The solution set is the empty set, \( \varnothing \).