Заполните таблицы для заданных функций, вычисляя значения y по формуле или находя x при известном y.

1. $y = x + 3$ Когда $x = -7$: $y = -7 + 3 = -4$ Когда $x = 0$: $y = 0 + 3 = 3$ Когда $x = 0,5$: $y = 0,5 + 3 = 3,5$ Когда $y = 13$: $13 = x + 3 \Rightarrow x = 13 - 3 = 10$ | x | -7 | 0 | 0,5 | 10 | |---|---|---|-----|----| | y | -4 | 3 | 3,5 | 13 | 2. $y = 2x - 1$ Когда $x = -3$: $y = 2(-3) - 1 = -6 - 1 = -7$ Когда $x = -1$: $y = 2(-1) - 1 = -2 - 1 = -3$ Когда $y = 9$: $9 = 2x - 1 \Rightarrow 2x = 10 \Rightarrow x = 5$ Когда $y = 8,2$: $8,2 = 2x - 1 \Rightarrow 2x = 9,2 \Rightarrow x = 4,6$ | x | -3 | -1 | 5 | 4,6 | |---|----|----|---|-----| | y | -7 | -3 | 9 | 8,2 | 3. $y = 5x + 4$ Когда $x = 0$: $y = 5(0) + 4 = 4$ Когда $y = -6$: $-6 = 5x + 4 \Rightarrow 5x = -10 \Rightarrow x = -2$ Когда $x = \frac{1}{5}$: $y = 5(\frac{1}{5}) + 4 = 1 + 4 = 5$ Когда $x = 3$: $y = 5(3) + 4 = 15 + 4 = 19$ | x | -2 | 0 | $\frac{1}{5}$ | 3 | |---|----|---|--------------|---| | y | -6 | 4 | 5 | 19 | 4. $y = -3x + 2$ Когда $x = -5$: $y = -3(-5) + 2 = 15 + 2 = 17$ Когда $x = \frac{1}{3}$: $y = -3(\frac{1}{3}) + 2 = -1 + 2 = 1$ Когда $x = 2,5$: $y = -3(2,5) + 2 = -7,5 + 2 = -5,5$ Когда $y = -22$: $-22 = -3x + 2 \Rightarrow -3x = -24 \Rightarrow x = 8$ | x | -5 | $\frac{1}{3}$ | 2,5 | 8 | |---|----|--------------|-------|---| | y | 17 | 1 | -5,5 | -22 | 5. $y = -10x - 1$ Когда $x = -1,5$: $y = -10(-1,5) - 1 = 15 - 1 = 14$ Когда $x = -0,3$: $y = -10(-0,3) - 1 = 3 - 1 = 2$ Когда $y = -6$: $-6 = -10x - 1 \Rightarrow -10x = -5 \Rightarrow x = 0,5$ Когда $x = 4$: $y = -10(4) - 1 = -40 - 1 = -41$ | x | -1,5 | -0,3 | 0,5 | 4 | |---|------|------|-----|---| | y | 14 | 2 | -6 | -41 | 6. $y = 0,5x + 5$ Когда $x = -3$: $y = 0,5(-3) + 5 = -1,5 + 5 = 3,5$ Когда $y = 4$: $4 = 0,5x + 5 \Rightarrow 0,5x = -1 \Rightarrow x = -2$ Когда $x = 2$: $y = 0,5(2) + 5 = 1 + 5 = 6$ Когда $x = 20$: $y = 0,5(20) + 5 = 10 + 5 = 15$ | x | -3 | -2 | 2 | 20 | |---|----|----|---|----| | y | 3,5 | 4 | 6 | 15 | 7. $y = \frac{2}{5}x - 3$ Когда $x = -5$: $y = \frac{2}{5}(-5) - 3 = -2 - 3 = -5$ Когда $y = -7$: $-7 = \frac{2}{5}x - 3 \Rightarrow \frac{2}{5}x = -4 \Rightarrow x = -4 \cdot \frac{5}{2} = -10$ Когда $x = 0$: $y = \frac{2}{5}(0) - 3 = -3$ Когда $x = 2,5$: $y = \frac{2}{5}(2,5) - 3 = \frac{2}{5}(\frac{5}{2}) - 3 = 1 - 3 = -2$ | x | -10 | -5 | 0 | 2,5 | |---|-----|----|---|-----| | y | -7 | -5 | -3 | -2 | 8. $y = \frac{3}{x} + 2$ Когда $x = -6$: $y = \frac{3}{-6} + 2 = -0,5 + 2 = 1,5$ Когда $y = 1$: $1 = \frac{3}{x} + 2 \Rightarrow \frac{3}{x} = -1 \Rightarrow x = -3$ Когда $x = -1$: $y = \frac{3}{-1} + 2 = -3 + 2 = -1$ Когда $x = 1$: $y = \frac{3}{1} + 2 = 3 + 2 = 5$ | x | -6 | -3 | -1 | 1 | |---|----|----|----|---| | y | 1,5 | 1 | -1 | 5 | 9. $y = -\frac{2}{x} - 4$ Когда $x = -2$: $y = -\frac{2}{-2} - 4 = 1 - 4 = -3$ Когда $x = -1$: $y = -\frac{2}{-1} - 4 = 2 - 4 = -2$ Когда $y = -5$: $-5 = -\frac{2}{x} - 4 \Rightarrow -\frac{2}{x} = -1 \Rightarrow x = 2$ Когда $x = 4$: $y = -\frac{2}{4} - 4 = -0,5 - 4 = -4,5$ | x | -2 | -1 | 2 | 4 | |---|----|----|---|-----| | y | -3 | -2 | -5 | -4,5 |