Math Problem Statement
Write a rational function with vertical asymptotes x = -4, x = 5 and an x-intercept of (-2,0).
Solution
To construct a rational function that satisfies the given conditions:
-
Vertical Asymptotes occur when the denominator equals zero. For vertical asymptotes at and , the denominator must have the factors and .
-
X-intercept occurs when the numerator equals zero. For an x-intercept at , the numerator must have the factor .
Putting these together, the rational function can be written as:
Here, is a constant that can be any non-zero value. If no specific value of is given, we can set for simplicity:
Let me know if you'd like further clarifications or details!
Related Questions:
- How can we determine horizontal asymptotes for this function?
- What happens to the function's behavior near the vertical asymptotes?
- What is the domain of this rational function?
- How would the graph of this function look?
- How do changes in the constant affect the function?
Tip: When writing rational functions, always double-check the placement of factors to ensure they satisfy the given conditions.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Rational Functions
Vertical Asymptotes
X-Intercepts
Algebra
Formulas
General form of a rational function: f(x) = N(x)/D(x), where N(x) and D(x) are polynomials.
Vertical asymptotes occur when D(x) = 0 (denominator is zero).
X-intercepts occur when N(x) = 0 (numerator is zero).
Theorems
The behavior of rational functions near vertical asymptotes.
Root theorem for finding x-intercepts.
Suitable Grade Level
Grades 10-12
Related Recommendation
Rational Function with Vertical Asymptotes at x = -2, x = 3 and Horizontal Asymptote y = 0
Construct a Rational Function with Given Asymptotes and Intercepts
Rational Function with Asymptotes and Intercepts
Create a Rational Function with Given Asymptotes and Intercepts
Rational Function with Zero at x=4 and Asymptotes at x=-2, x=3, y=5/3