Question

Give the domain, range, intercepts, asymptotes, intervals of increasing and decreasing, intervals of positive and negative, symmetry and extrema (if any) for the graph of this equation.
3/x^2-4 + 1

Answer 1

$y = \frac{3}{x^{2} - 4} + 1$

Domain: x² - 4 ≠ 0
                 + 4 + 4
                    x² ≠ 4
                 √x² ≠ √4
                    x ≠ ±2
           x ≠ -2 and x ≠ 2
     (-∞, -2) ∨ (-2, 2) ∨ (2, ∞)

Range: y ≠ 1
    (-∞, 1) ∨ (1, ∞)

Intervals: Increasing: (0.25 , ∞)
              Decreasing: (-∞, 0.25)

Symmetry: X-axis: Not Symmetric
                  Y-axis: Not Symmetric
                  Origin: Not Symmteric

Extrema: Maximum Relative: x = 0
                Minimum Relative: Nothing