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The Equation of a Rational Function has the Form,... f(x) = g(x)/h(x) where h(x) is not equal to zero.
We will use a given Rational Function as an Example to graph showing the Vertical and Horizontal Asymptotes, and also the Hole in the Graph of that Function, if they exist. Let the Rational Function be,...
f(x) = (x-2)/(x² - 5x + 6). f(x) = (x-2)/[(x-2)(x-3)].
Now if the Denominator (x-2)(x-3) = 0, then the Rational function will be Undefined, that is, the case of Division by Zero (0).
So, in the Rational Function f(x) = (x-2)/[(x-2)(x-3)], we see that at x=2 or x=3, the Denominator is equal to Zero (0). But at x=3, we notice that the Numerator is equal to ( 1 ), that is, f(3) = 1/0, hence a Vertical Asymptote at x = 3. But at x=2, we have f(2) = 0/0,
'meaningless'. There is a Hole in the Graph at x = 2.
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When you are given a graph how can you come up with a rational function equation?
You cannot, necessarily. Given a graph of the tan function, you could not.
Is a circle graph a function?
No, a circle graph is never a function.
How can you tell if a graph is a sine function or a cosine function?
sine graph will be formed at origine of graph and cosine graph is find on y-axise
Is the first derivative of a function is a constant then its graph is?
A line. The derivative of a function is its slope. If the slope is a constant then the graph is a line.
What is a derivative graph?
A derivative graph tracks the slope of a function.
When you are given a graph how can you come up with a rational function equation?
You cannot, necessarily. Given a graph of the tan function, you could not.
Why doesnt the graph of a rational function cross its vertical asymptote?
It can.
Why do we set the denominator to zero to graph a rational function?
We set the denominator to zero to find the singularities: points where the graph is undefined.
Can the graph of a rational function have more than one vertical asymptote?
Assume the rational function is in its simplest form (if not, simplify it). If the denominator is a quadratic or of a higher power then it can have more than one roots and each one of these roots will result in a vertical asymptote. So, the graph of a rational function will have as many vertical asymptotes as there are distinct roots in its denominator.
How you can use the zeros of the numerator and the zeros of the denominator of a rational function to determine whether the graph lies below or above the x-axis in a specific interval?
Discuss how you can use the zeros of the numerator and the zeros of the denominator of a rational function to determine whether the graph lies below or above the x-axis in a specified interval?
Can the graph of a rational function have both a horizontal and oblique asymptote?
Piece wise functions can do everything. Take two pieces of two rational functions, one have a horizontal asymptote as x goes to -infinity and the other have a slanted (oblique) one as x goes to +infinity. It is still a rational function.
What does an undefined graph look like?
An undefined graph typically occurs when there is a division by zero in a mathematical equation, resulting in an infinite or undefined value. In a graph, this would manifest as a vertical line or asymptote where the function approaches infinity or negative infinity. This can happen, for example, when plotting the graph of a rational function where the denominator equals zero at a certain point.
If the equation of a rational function is a rational expression is the function rational?
Yes. Rational functions must contain rational expressions in order to be rational.
If the equation of a function is a rational expressions the function is rational?
Yes. Rational functions must contain rational expressions in order to be rational.
If the equation of a function is a rational expression is the function rational?
Yes. Rational functions must contain rational expressions in order to be rational.
If the equation of a function is a rational expression the function is rational.?
Yes. Rational functions must contain rational expressions in order to be rational.
If the equation of a function is a rational expression the function is rational?
True
