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How do you find the horizontal asymptote in a graph of a rational function?
The horizontal asymptote is what happens when x really large. To start with get rid of all the variables except the ones with the biggest exponents. When x is really large, they are the only ones that will matter. If the remaining exponents are the same, then the ratio of those coefficients tell you where the horizontal asymptote is. For example if you have 2x3/3x3, then the ratio is 2/3 and the asymptote is f(x)=2/3 or y=2/3. If the exponent in the denominator is bigger, than y=0 is the horizontal asymptote. If the exponent in the numerator is bigger, than there is no horizontal asymptote.
What happens to the fraction if the numerator is increased?
If the numerator of the fraction is increased and the denominator doesn't change, then the value of the fraction increases.
What happens when decrease in numerator and increase in denominator?
The fraction gets smaller or increases, depending on whether the numerator and denominator are positive or negative.
What happens to a fraction that has the denomenator of 0 and numerator of 4?
The answer is "not a real number"
What happens if your numerator is bigger then your denominator?
It is then an improper or 'top heavy' fraction
How do you find the horizontal asymptote in a graph of a rational function?
The horizontal asymptote is what happens when x really large. To start with get rid of all the variables except the ones with the biggest exponents. When x is really large, they are the only ones that will matter. If the remaining exponents are the same, then the ratio of those coefficients tell you where the horizontal asymptote is. For example if you have 2x3/3x3, then the ratio is 2/3 and the asymptote is f(x)=2/3 or y=2/3. If the exponent in the denominator is bigger, than y=0 is the horizontal asymptote. If the exponent in the numerator is bigger, than there is no horizontal asymptote.
What happens to the fraction if the numerator is increased?
If the numerator of the fraction is increased and the denominator doesn't change, then the value of the fraction increases.
What do you mean by sum and product of the roots?
What is a "root"? A root is a value for which a given function equals zero. When that function is plotted on a graph, the roots are points where the function crosses the x-axis.For a function, f(x), the roots are the values of x for which f(x)=0. For example, with the function f(x)=2-x, the only root would be x = 2, because that value produces f(x)=0.Of course, it's easy to find the roots of a trivial problem like that one, but what about something crazy like this:Steps to find roots of rational functionsSet each factor in the numerator to equal zero.Solve that factor for x.Check the denominator factors to make sure you aren't dividing by zero!Numerator FactorsRemember that a factor is something being multiplied or divided, such as (2x-3) in the above example. So, the two factors in the numerator are (2x-3) and (x+3). If either of those factors can be zero, then the whole function will be zero. It won't matter (well, there is an exception) what the rest of the function says, because you're multiplying by a term that equals zero.So, the point is, figure out how to make the numerator zero and you've found your roots (also known as zeros, for obvious reasons!). In this example, we have two factors in the numerator, so either one can be zero. Let's set them both equal to zero and then solve for the x values:2x - 3 = 02x = 3x = 3/2ANDx + 3 = 0x = -3So, x = 3/2 and x = -3 become our roots for this function. They're also the x-intercepts when plotted on a graph, because y will equal 0 when x is 3/2 or -3.Denominator FactorsJust like with the numerator, there are two factors being multiplied in the denominators. They are x and x-2. Let's set them both equal to zero and solve them:x = 0ANDx - 2 = 0x = 2Those are not roots of this function. Look what happens when we plug in either 0 or 2 for x. We get a zero in the denominator, which means division by zero. That means the function does not exist at this point. In fact, x = 0 and x = 2 become our vertical asymptotes (zeros of the denominator). So, there is a vertical asymptote at x = 0 and x = 2 for the above function.Here's a geometric view of what the above function looks like including BOTH x-intercepts and BOTH vertical asymptotes:
How vertical erosion happens?
it s bent
What happens when decrease in numerator and increase in denominator?
The fraction gets smaller or increases, depending on whether the numerator and denominator are positive or negative.
What happens to a fraction that has the denomenator of 0 and numerator of 4?
The answer is "not a real number"
What happens when you multiply a fraction by minus one?
The numerator changes sign.
What happens if your numerator is bigger then your denominator?
It is then an improper or 'top heavy' fraction
What happens if earths axis were vertical?
There would be no seasons.
In rational functions what happens when w gets close to zero?
The answer depends on what w represents. If w is the denominator of the rational function then as w gets close to zero, the rational function tends toward plus or minus infinity - depending on the signs of the dominant terms in the numerator and denominator.
What happens to the value of a fraction when you double its denominator?
You have to double the numerator, but the value of the fraction remians the same but if you dont double the numerator then you dont have the same fraction
What happens when you multiply both a numerator and a denominator of a fraction by 4?
You will get an equivalent fraction.
