# asymptote and domain of rational function

1. Write an equation that expresses the relationship. Use k as the constant of variation. d varies directly as the square of y.

2. Find the horizontal asymptote, if any, of the graph of the rational function. f(x) = 8x / (2x^2 + 1)

3. Find the domain of the rational function: g(x) = 6x / [(x-1)(x+7)]

4. Find the vertical asymptotes, if any, of the graph of the rational function: f(x) = x/(x^2 +4)

5. How many vertical asymptotes are possible for the rational function R(x)?

6. Find the domain of the rational function. g(x) = (x+ 4)/(x^2 - 4)

7. Choose the one alternative that best completes the statement or answers the equation.

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. 5x^2 - 3x >=8

8. Find the indicated intercepts of the graph of the function

9. Find the vertical asymptotes, if any, of the graph of the rational function: f(x) = x/[x(x-2)]

10. Let R(x) = (x^3 - 2x^2 - 7)/(x^2 + 1), what kinds of asymptotes does R(x) possess?

11. Use the graph of the rational function shown to complete the statement. As x-->2-, f(x)-->

12. Find the horizontal asymptote, if any, of the graph of the rational function: h(x) = 6x^3/(3x^2 + 1)

13. what is the equation of the slant asymptote for R(x) = (x^2 - x + 17) /(x^2 + 1)?

14. If R(x) is a rational function, then R(x) < 0 describes what?

15. Is there y-axis symmetry for the rational function f(x) = -4x^2 /(6x^4 - 3)?

16. Find the indicated intercept of the graph of the function: x-intercepts of f(x) = (x - 4)/(x^2 + 8x - 2)

17. is there origin symmetry for the rational function f(x) = 4x / (6x^2 + 1)?

18.y varies jointly as a and b and inversely as the square root of c. y = 48 when a = 4, b = 8, and c = 36. Find y when a = 2, b = 7, and c = 16.

19. solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. (x + 9) /(x + 1) > 0

20. Find the horizontal asymptote, if any, of the graph of the rational function: g(x) = 6x^2 /(2x^2 + 1)

#### Solution Summary

The solution provides detailed steps of finding the domain, intercepts, and asymptotes of the rational function.