Sketch the asymptotes and graph the function y=6/(x-2)+4
2 answers:
Answer:
Step-by-step explanation:
We have to sketch the asymptotes of the given function y = 6/(x -2) + 4
1) For horizontal asymptotes
In the given function y = 6/(x -2) is in the form of
Degree of x in numerator is lower than denominator therefore horizontal asymptote is y = 0
Since y = 6/(x -2) is shifted 4 upwards so horizontal asymptote for the shifted function will be y = 0+4 = 4
2) For vertical asymptotes
We will put the denominator of the function equal to the zero.
(x - 2) = 0
x = 2 is the vertical asymptote.
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Answer:
M = (8,9)
Step-by-step explanation:
Notice that the points (0,15), and (20,0) form with the origin of coordinates (0,0), a right angle triangle (please see attached image). This triangle has twon perpendicular sides of length 15 and 20 respectively. Therefore, we can find the length of the segment that joins points A (0,15) and B (20,0) by finding the length of the hypotenuse in a right angle triangle (with the Pythagorean Theorem):
Now, to get a 2:3 proportion on Segment AB which is of length 25, we need to divide it in five equal parts (see the picture on the right of the attached image), and place point M at two of these divisions from point A (0,15) and along segment AB.
In order to find the appropriate location in (x,y) coordinates, we consider a smaller triangle (pictured in orange in the image) that is similar to the first larger triangle (pictured in blue). Notice that if the length of AB is 25, each of its five equal divisions would be of length "5", and therefore two of them will render a length of "10" (which is the hypotenuse of this smaller right angle triangle.
Now, in order to find the sides of this smaller triangle (which can give us the clues on the horizontal and vertical coordinates of point M), we can use proportions.
To find the length "x" of the horizontal side , we do:
To find the length "y" of the vertical side , we do:
Then, the coordinate "x" of point M will be "8", while we can calculate the y position of point M subtracting "6" from 15 (the length of the vertical side in the original triangle). This gives us the coordinates (8,9) for point M as marked in orange in the picture.
