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 = (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