Math Problem Statement

y = (x^2 + 3x) / (x - 1)

Solution

The function provided in the image is:

y=x2+3xx−1y = \frac{x^2 + 3x}{x - 1}

If you would like to analyze this function, there are several directions we could explore. For example, we could find:

  1. The domain and range of the function.
  2. Any asymptotes, both vertical and horizontal.
  3. The derivative y′y' for finding slopes and critical points.
  4. The behavior of yy as x→∞x \to \infty or x→−∞x \to -\infty.
  5. Points of discontinuity or special behavior.

Would you like to explore one of these aspects or have a specific question about this function?

Relative Questions

  1. How do we find the domain of a rational function?
  2. What are the steps to determine vertical and horizontal asymptotes?
  3. How can we apply differentiation to find critical points in this function?
  4. How does the behavior of the function change near points of discontinuity?
  5. What are possible applications of this type of function in real-life scenarios?

Tip: For rational functions, always start by identifying points where the denominator is zero to understand discontinuities and asymptotes.

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Math Problem Analysis

Mathematical Concepts

Rational Functions
Algebra
Calculus

Formulas

Rational function y = (f(x)) / (g(x))
Vertical asymptote at x = a when denominator g(x) = 0
Horizontal asymptote as x approaches infinity or negative infinity
Derivative of rational functions

Theorems

Limits and Continuity
Differentiation for critical points
Behavior of functions at asymptotes

Suitable Grade Level

Grades 10-12

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