intercepts of f(x)=(x^2)/(x^2+16)
On the horizontal axis, y = 0: solve x2x2 + 16 = 0
1) Let's solve in ℝ: x2x2 + 16 = 0
A quotient is zero if and only if its numerator is zero and its denominator is not: we solve the numerator equal to 0
⇥1.1) Let's solve in ℝ: x2 = 0
⇥x2 = 0 means that: x = 0
⇥Solution obtained: x = 0
⇥1.2) To prevent the denominator from being zero, let's solve: x2 + 16 ≠ 0
⇥ x2 ≠ -16
⇥In ℝ, a square is never negative: no real number has -16 as its square
⇥Solution: x ∈ ∅
The graph crosses the horizontal axis at (0, 0)
On the vertical axis, x = 0: calculate f(0)
⇥ 0202 + 16
⇥ⓘ Adding 0 changes nothing: 0 + 16 = 16
⇥ 0
▶Axis intercepts:   (0, 0)