True or False?: To make a sketch of any rational function whose numerator is a number and whose denominator is a factored polyno
mial, use the following rule of thumb.
The function has a vertical asymptote at every x-value where its denominator is zero, and the function is always negative between two asymptotes.
The function has a vertical asymptote at every x-value where its denominator is zero, and the function is always negative between two asymptotes.
2 answers:
The question is for any rational function. I give one example in picture below. There we can see that first part of the "rule" is true. we indeed have vertical asymptotes at every x value where denominator is zero in this case x = 3 and x = 1. but second part of the rule is not true. we can see that if we inverse x ( we have factor that looks like a - x we get positive function between asymptotes.
Answer is False
Answer is False
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Answer:
The rule that represents the function is therefore the function is
Step-by-step explanation:
We have 5 ordered pairs in the plane xy. This means that <em>every pair has the form (x, y).</em>
Then, we have 5 values of x, which will give us 5 values of y, using the rule that represents the function.
<u>The easy evaluation is that when x=0, the value of y is y=1,</u> and then we can evaluate the rule for x=-1, and x=1, <em>the value of y is the same, y=2</em>. We can see here that we have a parabolic function, that is not centered in the origin of coordinates because when x=0, y=1.
So <u>we propose the rule </u><u> which is correct for the first 3 values of x.</u>
Now, <em>we evaluate the proposed rule when x=2, and when x=3</em>. This evaluations can be written as
Therefore, the rule is correct, and the function is