intercepts of f(x)=(x^2-16)/(x+4)

On the horizontal axis, y = 0: solve

\frac{x^{2} - 16}{x + 4} = 0

⇥1) Let's solve in

ℝ

\frac{x^{2} - 16}{x + 4} = 0

⇥Using the formula:

a^{2} - b^{2} = (a - b) \cdot (a + b)

, we divide the numerator and denominator of

\frac{x^{2} - 16}{x + 4}

by the common factor:

x + 4

, which gives the new expression:

x - 4

⇥

x - 4 = 0

⇥ⓘ We add

4

to both sides

⇥Candidates, pending the domain check:

x = 4

⇥2) Let's find the domain of

\frac{x^{2} - 16}{x + 4} = 0

⇥ For the expression

\frac{x^{2} - 16}{x + 4}

to be defined, we must have:

x + 4 \neq 0

⇥ⓘ We subtract

4

from both sides

⇥Domain constraints:

x \neq -4

The graph crosses the horizontal axis at

(4, 0)

On the vertical axis, x = 0: calculate f(0)

⇥

\frac{0^{2} - 16}{0 + 4}

⇥ⓘ Adding 0 changes nothing:

0 - 16

-16

0 + 4

4

■We simplify the fraction by dividing the numerator and the denominator by

4

, their greatest common divisor:

- \frac{16}{4}

-4

⇥

-4

▶Axis intercepts:

{(4, 0), (0, -4)}