Mathematics, 04.02.2020 15:03 jeanieb

20 ! !

a meteorologist announces that yesterday's high temperature was within 4 degrees celsius of 18 degrees celsius all across the country. write an inequality that involves an absolute value to represent yesterday's high temperature. solve the inequality and explain the meaning of the solution.

lx-18l is less than or equal to 4
x-18< =4 x-18< =-4
x-18+18< =4+18 x-18+18< =-4+18
x< =22 or x< =14
14< =x< =22
is this correct?

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Answer from: nia454

Your answer is correct in the sense that 14 ≤ x ≤22 since the temperature is 18 ° plus/minus 4°. However, the wording of the problem implies that it wants your final answer in terms of absolute value.

Based on your work, you understand the basics of the problem, and you correctly expressed it as an inequality. The problem is how to express it with an absolute value and only one inequality sign.

The word "within" implies that ≤ is the correct symbol, rather than < (you were correct to use that symbol)

We can word the expression in this way: The difference between the real temperature and 18° is less than or equal to 4. Difference in this sense is a positive number whether the real temperature is lower or higher than 18, so absolute value is implied.

We can express it mathematically this way:
|18-x| ≤ 4

Plug a few numbers in for X to make sure it makes sense.
If X equals 16 (within the range), |18-16| = 2, which is less than 4
If X equals 20, |-2| equals 2, which is less than 4
If X equals 10, |18-10| = 8, does not comply with our inequality.

Answer from: Quest

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

Me if you can and if you finished this lesson on edg- comment you.

Answer from: Quest

well my understanding of this question is they want you to use the y=14.1x -2.3 and put the coordinates they gave you onto the line segment of y=14.1x -2.3

step-by-step explanation:

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