821 Вправа 821Алгебра 8 клас Тарасенкова 2025 · § 20 · стор. 244

821. Побудуйте графік функції: у = (х² − 2х − 3)/(х − 3).

ОДЗ: ${\displaystyle x-3\ne 0}$; ${\displaystyle x\ne 3}$;

${\displaystyle x^2-2x-3=}$${\displaystyle 0}$;

${\displaystyle x_1+x_2=}$${\displaystyle 2}$; ${\displaystyle x_1\cdot x_2=}$${\displaystyle -3}$;

${\displaystyle x_1=}$${\displaystyle 3}$; ${\displaystyle x_2=}$${\displaystyle -1}$;

${\displaystyle x^2-2x-3=}$${\displaystyle (x-3)(x+1)}$;

${\displaystyle y=}$${\displaystyle \frac{x^2-2x-3}{x-3}=}$${\displaystyle \frac{\cancel{\left(x-3\right)}(x+1)}{\cancel{\left(x-3\right)}}=}$${\displaystyle x+1}$;

виколота точка: ${\displaystyle x=}$${\displaystyle 3}$, ${\displaystyle y=}$${\displaystyle 3+1=}$${\displaystyle 4}$, ${\displaystyle \left(3;4\right)}$;

${\displaystyle y=}$${\displaystyle x+1}$: