Explain why it is correct to claim that A/B < B/A is true.
1 answer:
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We are given a set of data depicting the number of books read by students.
We are required to find the mode of the data.
In order to find the mode, we simply need to count each unique number and know how many times each number occurs.
The unique number with the largest frequency of occurence is the mode of the data.
The data given is:
We will represent each count for the unique numbers with a frequency table showing each unique number and the number of times it occurs.
This table is done below:
Answer:
y = 1 + 1/((x -1)(x -4))
Step-by-step explanation:
To get vertical asymptotes at 1 and 4, you need factors (x -1) and (x -4) in the denominator. As x approaches 1 or 4, one of these will approach zero, and the function value will approach infinity.
To get a horizontal asymptote of 1, the function must approach the value 1 when the value of x gets large (positive or negative). This can generally be accomplished by simply adding 1 to a fraction that approaches zero when x is large.
Here, we make the fraction be the one that gives the vertical asymptotes, and we simply add 1 to it.
... y = 1 + 1/((x -1)(x -4))
If you like, this can be "simplified" to ...
... y = (x² -5x +5)/(x² -5x +4)
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In this rational expression form, please note that the numerator and denominator have the same degree. That will be the case when there is a horizontal asymptote. (When a slant asymptote, the numerator degree is 1 higher than the denominator.) The ratio of the coefficients of the highest degree terms is the horizontal asymptote value (or the slope of a slant asymptote).
