Determine the least possible degree of the function corresponding to the graph shown below. Justify your answer.
The graph is attached. I remade the graph using google grapher, but the graph I got in the test have exactly the same x-intercepts (-2 of order 2 and 1 of order 3), y-intercepts, turning points, and end behaviour.
The Attempt at a Solution
So according to the x-intercept, the least possible degree is 5. (adding up the order of the x-intercepts, 2+3=5.
According to the turning points, the least possible degree is 3. (2 turning points, 2+1=3.)
Because the question asks for the least possible degree, I thought I should use the larger value here, which is 5.
But then my teacher said the answer is 3, because 3 is less than 5. The class also got 3 as answer. When I asked my math teacher about this she told me that the question asked about the least degree, so since 3 is less than 5, the answer should have been 3. she said "5 is the exact degree, not the least degree." Some of my classmates also told me that since her question was regarding the "least" degree, I should've put 3 instead of 5.
And this just completely baffles me-the question clearly says the least possible degree. So for it to be the least possible degree, it has to be possible first. The x-intercepts clearly indicate that it would not be even possible for the function to be a 3rd degree function.
I was told that when my English improves I will understand the question better and then see why the answer is 3. But I have literally thought about the question for a week now and still don't see the flaw in my logic. Please help me understand this question? Sorry and Thanks in advance.
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