Відповіді на вправи: 453 (1)

453. Побудуйте графік функції:

1) у = $\frac{{х}^3-2х}{х}$ = х² – 2;

х	0	2	–2
у	–2	2	2

y(0) = –2; y(2) = 2; y(–2) = 2; x₀ = –2.

2) y = $\frac{x^4+{4x}^3}{x^2}$ = x(x + 4) = x² + 4;

x₀ = $\frac{-b}{2a}$; x₀ = –2;

y₀ = 4 + 4(–2) = –4;

x	0	–2	1	–4
y	0	–4	5	0

y = x² + 4x; y(1) = 5; y(–4) = 0.

3) y = $\frac{{2x}^3-{4x}^2+5x}{x}$ = 2x² – 4x + 5;

x₀ = 1; y₀ = 3.

x	0	2	–1
y	5	5	11

y(0) = 5;

y(2) = 2 • 4 – 4 • 2 + 5 = 5;

y(–1) = 2 • 1 + 4 + 5 = 11.

4) y = $\frac{x^3+8}{x+2}$ = $\frac{(x+2)(x^2-2x+4)}{x+2}$ = x2 – 2x + 4;

x₀ = 1; y₀ = 1 + (–2) + 4 = 3.

x	0	2	–1
y	4	4	7

y(0) = 4, y(2) = 4, y(–1) = 7.