Answers: choice A and choice D
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Step-by-step explanation:
I'll go through the five answer choices and say whether they are true or false, and why that is the case.
Choice A is true because the greatest integer function, aka the floor function, is a function that takes any decimal number and rounds it down to the nearest whole number. For example, if the input is x = 2.8 then f(x) = f(2.8) = 2.
Choice B is false. This function is not one-to-one because we can draw a horizontal line through more than one point on this graph.
Choice C is false. This is not an absolute value function. The absolute value graph is a V shaped graph.
Choice D is true. If you use the given graph, you would locate x = -3.4 on the x axis, draw a vertical line until you reach the stair-step graph, then draw a horizontal line to the y axis. Note how you arrive at y = -4. Check out figure 1 in the attached images below. We round down to the nearest whole number. I recommend drawing out a vertical number line as shown in the attached image below (figure 2).
Choice E is false. See the attached image. The proper equation should be f(4.9) = 4. Check out figure 3.