1092 Вправа 1092Алгебра 8 клас Бевз 2025 · § 21 · стор. 205

1092. Побудуй графік функції. а) y = (x² − x − 6)/(x − 3); б) y = (2x² − 9x − 5)/(5 − x).

а) ОВ: ${\displaystyle x\ne 3}$;

${\displaystyle x^2-x-6}$: ${\displaystyle x_1+x_2=}$${\displaystyle 1}$;

${\displaystyle x_1{x}_2=}$${\displaystyle -6}$ → ${\displaystyle x_1=}$${\displaystyle 3,x_2=}$${\displaystyle -2}$;

${\displaystyle x^2-x-6=}$${\displaystyle \left(x-3\right)\left(x+2\right)}$;

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

Графік — пряма ${\displaystyle y=}$${\displaystyle x+2}$ без точки ${\displaystyle (3;5)}$:

б) ОВ: ${\displaystyle x\ne 5}$;

${\displaystyle 2x^2-9x-5}$: ${\displaystyle D=}$${\displaystyle {(-9)}^2-4\cdot 2\cdot (-5)=}$${\displaystyle 121}$;

${\displaystyle x_{1,2}=}$${\displaystyle \frac{9\pm 11}{4}}$;

${\displaystyle x_1=}$${\displaystyle 5}$;

${\displaystyle x_2=}$${\displaystyle -0,5}$;

${\displaystyle 2x^2-9x-5=}$${\displaystyle 2(x-5)(x+0,5)=}$${\displaystyle \left(x-5\right)\left(2x+1\right)}$;

${\displaystyle y=}$${\displaystyle \frac{\cancel{\left(x-5\right)}(2x+1)}{-\cancel{\left(x-5\right)}}=}$${\displaystyle -2x-1}$;

Графік — пряма ${\displaystyle y=}$${\displaystyle -2x-1}$ без точки ${\displaystyle (5;-11)}$: