Math Problem Statement

f(x) = (2x^2+7x+5)/(3x^2-1x-10); This function has:

  1. A y-intercept at the point

  2. x-intercepts at the point(s)

  3. Vertical asymptotes at x =

Solution

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Math Problem Analysis

Mathematical Concepts

Rational Functions
Quadratic Equations
Intercepts
Asymptotes

Formulas

Y-intercept: f(0)
X-intercepts: Set the numerator equal to zero
Quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / 2a
Vertical Asymptotes: Set the denominator equal to zero

Theorems

Quadratic Formula
Asymptote Behavior in Rational Functions

Suitable Grade Level

Grades 10-12