A) The y intercept is (0,-18)
This is true.
The x value x = 0 leads to the y value y = -18. See row 1 of the table. Keep in mind that y = f(x).
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B) The max value of the function is 4
This is false.
The largest y or f(x) value shown is y = 70 which is in the last row of the table. There could be other larger y values, but we dont need to find them as all we need to do is find a counter-example to disprove the initial claim.
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C) A local minimum is located within the interval 3 <= x <= 6
This is true.
When we go from x = 3 to x = 6, the function decreases for a bit, then it starts to increase. This change from decreasing to increasing means that the function bottoms out somewhere forming a valley, ie a local min.
Visually, it might help to plot the points as shown in the attached image below. We see that the local min could be around point F somewhere or perhaps point F itself is the local min.
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D) A local max is in the interval 1 <= x <= 3
This is true.
This is similar to part C above, but now we're looking to see if we transition from increasing to decreasing. In this case this happens. So somewhere in the interval from x = 1 to x = 3 is a local max point.
Visually the point C could be the local max (see attached image below) as this is one potential spot where the function curve reaches its highest peak in this very specific region/interval. Some math books will use the term "neighborhood" in place of "interval" and it means effectively the same thing.
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E) The function is increasing on the interval 6 <= x <= 8
This is true.
Refer to the graph below. Note how the points go up as we move from left to right. In other words, the y values are increasing as we increase the x values from x = 6 to x = 8.
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Final Answer:
There are 4 true answers and they are: choice A, choice C, choice D, choice E
A shorter way to say this is to say "only choice B is false while the rest are true".
