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The graph shows the function 𝑓(𝑥) = 𝑥² − 2𝑥 + 3. What is the solution set of 𝑓(𝑥) = 0?

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.

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