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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.
