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The graph shows the function 𝑓(𝑥) = 2𝑥² − 4𝑥 − 6. What is the solution set of 𝑓(𝑥) = 0? What is the solution set of 𝑓(𝑥) = −6?

The graph shows the function 𝑓 of 𝑥 is equal to two 𝑥 squared minus four 𝑥 minus six. What is the solution set of 𝑓 of 𝑥 equals zero? What is the solution set of 𝑓 of 𝑥 equals negative six?

The solution set of 𝑓 of 𝑥 equals zero is the set of values of 𝑥 for which the curve crosses the 𝑥-axis, since 𝑦 equals zero at these points. Inspecting the graph, we can see that the curve crosses the 𝑥-axis at two points: 𝑥 equals negative one and 𝑥 equals three. Therefore, the solution set of 𝑓 of 𝑥 equals zero is negative one, three.

Just as the solution of 𝑓 of 𝑥 equals zero is the set of values for which 𝑦 equals zero, the solution set of 𝑓 of 𝑥 equals negative six is the set of values where 𝑦 equals negative six. We can find this by drawing a horizontal line at 𝑦 equals negative six and determining the coordinates of the points where the line and curve intersect. We can identify from the graph that the points of intersection are at 𝑥 equals zero and 𝑥 equals two. Therefore, the solution set of 𝑓 of 𝑥 equals negative six is zero, two.

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