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College Algebra and Trigonometry1st EditionDonna Gerken, Julie Miller 9,697 solutions Algebra and Trigonometry1st EditionJay Abramson 6,339 solutions Algebra and Trigonometry9th EditionMichael Sullivan 10,535 solutions Algebra and Trigonometry9th EditionMichael Sullivan 10,535 solutions Video TranscriptHi. So he wants to know which of the following rational functions this graph below. Okay, so, the important part of these is the vertical of symptoms. Okay, vertical ascent owes me these, like, checkered lines that are basically saying that the function, which is the orange stuff never actually crosses these lines. And they get really close. Like this meaning is it gets really close but never actually crosses the checkered line here. It gets really close and notice since, like that says negative 10. And like, that means each of these dashes counts too. So, there isn't a vertical of symptom at negative four and it looks like there's a vertical substitute that halfway between zero and two and that's one. Now, vertical sometimes happen when you have, like X values and denominator and it's basically and you can't really have zero the denominator ever. So, the answer is B because this is saying, like, all right, if you make X negative four, you get zero in the denominator, which is bad. That's that's why there's a vertical ascent to negative four here, X minus one means if you make X one, you get zero and the denominator and that you can't do that. So, that's why there is a vertical sento at one. Okay, that's what the answer is. B. I also grafted to like, grafted in demos and look the same stuff. Exactly right. Whoa Which is a rational function?A rational function is one that can be written as a polynomial divided by a polynomial. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator. Example 1. f(x) = x / (x - 3). The denominator has only one zero, x = 3.
Which is a rational function y x 2 3x 5?y=x2−3x+5 y = x 2 − 3 x + 5 . Because of the form that this function has, it is a quadratic function since they are represented in the following way y=ax2+bx+c y = a x 2 + b x + c , therefore it is not a rational function.
What is a rational function on a graph?Rational functions are of the form y=f(x) , where f(x) is a rational expression . Some of the examples of rational functions are: y=1x , y=xx2 − 1 , y=3x4 + 2x + 5. The graphs of the rational functions can be difficult to draw.
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