Monday

July 28, 2014

July 28, 2014

Posted by **Amanda** on Sunday, November 28, 2010 at 8:11pm.

r(x)= x^6 +10 / x^4+8x^2+15

has no x intercept and no horizontal, vertical, or slant asymptote. What is its end behaviour?

Please help? thankq

- Math -
**MathMate**, Sunday, November 28, 2010 at 9:52pmHorizontal/slant intercepts:

divide the leading coefficient of the numerator by that of the denominator:

q=x^6/x^4=x²

If q is a numerical constant, the horizontal asymptote is at y=q.

If q is a linear term, such as 2x, then there is a slant asymptote along the line y=2x.

Vertical asymptotes occur where the denominator becomes zero.

Substitute y=x² in the denominator and solve for the resulting quadratic where y=-3 or -5. Clearly the solutions for x in y=-3 or -5 are complex, therefore the denominator does not become zero, hence no vertical asymptote.

**Related Questions**

Gr.11 - Rational functions graphing. - 1. Identify a rational function whose ...

algebra - find the slant asymptote of the graph of the rational function and use...

Precalculus - Write an equation for rational function with given properties. a...

Math - Analyze the function algebraically. List its vertical asymptotes, holes, ...

Calculus - Which of these rational functions has a ) horizontal asymptote? a ...

PreCalculus - State the Vertical Asymptote, Horizontal Asymptote, domain, range...

math - 5. State a rational function that satisfies all of the following: The y...

math help please... - 1.Explain how to find the equation of the vertical ...

math - how do you create a function that has a graph with the given features: a...

College Algebra - 1.Use completing the square to describe the graph of the ...