Video Transcript
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?
Here, we have been given the
explicit function that describes 𝑓 of 𝑥, but since we have the graph, we can
simply solve the equation graphically without factoring or using the quadratic
formula. Recall that the solution set of
𝑓 of 𝑥 equals zero can be found by identifying the points 𝑥, 𝑦 on the graph
where 𝑦 is equal to zero, which is where the curve intersects the 𝑥-axis. In this case, however, the
curve is entirely above the 𝑥-axis. For this reason, there are no
points at which 𝑦 equals zero. Hence, there are no real values
of 𝑥 that solve the equation. So the solution set is the
empty set, denoted as shown.
