Max is trying to prove to his friend that two reflections, one across the x-axis and another across the y-axis, will not result
in a reflection across the line y = x for a pre-image in quadrant II. His friend Josiah is trying to prove that a reflection across the x-axis followed by a reflection across the y-axis will result in a reflection across the line y = x for a pre-image in quadrant II. Which student is correct, and which statements below will help him prove his conjecture? Check all that apply
Max is correct.
Josiah is correct.
If one reflects a figure across the x-axis from quadrant II, the image will end up in quadrant III.
If one reflects a figure across the y-axis from quadrant III, the image will end up in quadrant IV.
A figure that is reflected from quadrant II to quadrant IV will be reflected across the line y = x.
If one reflects a figure across the x-axis, the points of the image can be found using the pattern (x, y) (x, –y).
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) (–x, y).
Taking the result from the first reflection (x, –y) and applying the second mapping rule will result in (–x, –y), not (y, x), which reflecting across the line should give.
Max is correct.
Josiah is correct.
If one reflects a figure across the x-axis from quadrant II, the image will end up in quadrant III.
If one reflects a figure across the y-axis from quadrant III, the image will end up in quadrant IV.
A figure that is reflected from quadrant II to quadrant IV will be reflected across the line y = x.
If one reflects a figure across the x-axis, the points of the image can be found using the pattern (x, y) (x, –y).
If one reflects a figure across the y-axis, the points of the image can be found using the pattern (x, y) (–x, y).
Taking the result from the first reflection (x, –y) and applying the second mapping rule will result in (–x, –y), not (y, x), which reflecting across the line should give.
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Here are 3 questions with their respective answers.
1) Find
Answer: 4.
Explanation:
This expression indicates the limit as the function f(x) approaches 2 from the right side.
You should apply the function (the line) from the right side of 2 and get as close to x = 2 as you can.
That line has an open circle at y = 4, which is the limit we are looking for.
2) Analyze the graph to see if the limit exists.
Answer:
To find each limit, utilize the function approaching from the direction of x.
It's important to note that since the two limits differ, it is concluded that the limit of the function as x approaches 2 does not exist.
3)
Answer: -1
To determine the limit as the function approaches 3 from the left, follow the line ending with an open circle at (3, -1).
Hence, the limit is -1.
1) Find
Answer: 4.
Explanation:
This expression indicates the limit as the function f(x) approaches 2 from the right side.
You should apply the function (the line) from the right side of 2 and get as close to x = 2 as you can.
That line has an open circle at y = 4, which is the limit we are looking for.
2) Analyze the graph to see if the limit exists.
Answer:
To find each limit, utilize the function approaching from the direction of x.
It's important to note that since the two limits differ, it is concluded that the limit of the function as x approaches 2 does not exist.
3)
Answer: -1
To determine the limit as the function approaches 3 from the left, follow the line ending with an open circle at (3, -1).
Hence, the limit is -1.