intercepts of f(x)=(x-6)/(x+3) — step-by-step solution

On the horizontal axis, y = 0: solve

\frac{x - 6}{x + 3} = 0

1) Let's solve in

ℝ

\frac{x - 6}{x + 3} = 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

x - 6 = 0

⇥Candidates, pending the domain check:

x = 6

⇥1.2) To prevent the denominator from being zero, let's solve:

x + 3 \neq 0

⇥Domain condition:

x \neq -3

For the expression

\frac{x - 6}{x + 3}

to exist, you must check:

x + 3 \neq 0

Domain constraints:

x \neq -3

The graph crosses the horizontal axis at

(6, 0)

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

⇥

\frac{0 - 6}{0 + 3}

⇥ⓘ Adding 0 changes nothing:

0 - 6

-6

0 + 3

3

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

3

, their greatest common divisor:

- \frac{6}{3}

-2

⇥

-2

▶Axis intercepts:

{(6, 0), (0, -2)}