Simple Graphing rational expressions question

In summary, to find the point where a graph crosses the oblique asymptote, you first need to find the equation of the oblique asymptote in the form f(x) = (ax+b) + (g(x)/h(x)). Then, as x approaches infinity, the g(x)/h(x) term will approach 0, resulting in f(x) approaching ax+b. This is the equation of the oblique asymptote. However, the oblique asymptote does not intersect with the graph, so there is no specific point where they cross.
  • #1
xCanx
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0
How do you find the point where the graph crosses the oblique asymptote?
 
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  • #2
If you mean how to find an oblique asymptote of a function. you basically get it into the form

[tex]f(x)=(ax+b) + \frac{g(x)}{h(x)}[/tex]

and then as [tex]x\rightarrow \infty, \frac{g(x)}{h(x)}\rightarrow 0[/tex]
and so [tex]f(x)\rightarrow ax+b[/tex] and that it is the oblique asymptote
 
  • #3
I know how to find the oblique asymptote, but my question was how to find the point on the oblique asymptote where the graph crosses.

When it switches sides.
 
  • #4
xCanx said:
I know how to find the oblique asymptote, but my question was how to find the point on the oblique asymptote where the graph crosses.

When it switches sides.
Unreasonable. The asymptote contains no point of the graph; the asymptote does not intercept the graph.
 

What is a rational expression?

A rational expression is a fraction where the numerator and denominator are polynomials. It is also known as a rational function.

What is the graph of a rational expression?

The graph of a rational expression is a set of points on a coordinate plane that represent the values of the expression for different input values. It can be a line, curve, or a combination of both.

How do you graph a rational expression?

To graph a rational expression, you can follow these steps:1. Simplify the expression if possible.2. Identify the vertical and horizontal asymptotes.3. Plot the intercepts by setting the numerator and denominator equal to zero.4. Choose additional points to plot.5. Connect the points with a smooth curve or line.

What is the significance of asymptotes in the graph of a rational expression?

Asymptotes are important in the graph of a rational expression because they indicate where the graph will approach but never touch. Vertical asymptotes occur where the denominator is equal to zero, while horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator.

How do you find the domain and range of a rational expression?

The domain of a rational expression is all the possible input values that make the expression defined. To find it, set the denominator equal to zero and solve for the variable. The range of a rational expression is all the possible output values. To find it, consider the behavior of the graph and use interval notation to express the range.

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