The graph shows the function 𝑓 of
𝑥 equals 𝑥 squared minus two 𝑥 plus three. What is the solution set of 𝑓 of
𝑥 equals zero?
If we’re looking for 𝑓 of 𝑥 equal
to zero, we’re looking for the 𝑥-values that make 𝑥 squared minus two 𝑥 plus
three equal to zero. And on the graph, that will be the
place where 𝑦 equals zero. And we know that 𝑦 equals zero
along the 𝑥-axis. In order for this function to have
a solution of 𝑓 of 𝑥 equals zero, it would need to cross the 𝑥-axis. This function does not cross the
𝑥-axis. Therefore, it has zero solutions or
zero roots. And therefore, the solution set
here is the empty set; there is no solution.