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МатематикаВопрос:
Fill in the table with the values of the given functions at specified points. The functions are: 1) y = x^2 + x - 1, 2) y = x^2 + x + 6, 3) y = x^2 + 2x - 3, 4) y = x^2 + 3x + 4, 5) y = 2x^2 - x - 7, 6) y = -3x^2 - x + 20, 7) y = sqrt(3 - x), 8) y = sqrt(2x - 5), 9) y = -8 * sqrt(-x + 4), 10) y = |x| + 3, 11) y = |x| - 8, 12) y = -|x|, 13) y = |x + 3|, 14) y = |x - 5|. The points are f(3), f(0), f(-2).
Ответ:
Решение:
Заполним таблицу, подставляя заданные значения x в функции.
| № | \( y = f(x) \) | \( f(3) \) | \( f(0) \) | \( f(-2) \) |
|---|---|---|---|---|
| 1) | \( y=x^2+x-1 \) | \( 3^2+3-1 = 9+3-1 = 11 \) | \( 0^2+0-1 = -1 \) | \( (-2)^2+(-2)-1 = 4-2-1 = 1 \) |
| 2) | \( y=x^2+x+6 \) | \( 3^2+3+6 = 9+3+6 = 18 \) | \( 0^2+0+6 = 6 \) | \( (-2)^2+(-2)+6 = 4-2+6 = 8 \) |
| 3) | \( y=x^2+2x-3 \) | \( 3^2+2(3)-3 = 9+6-3 = 12 \) | \( 0^2+2(0)-3 = -3 \) | \( (-2)^2+2(-2)-3 = 4-4-3 = -3 \) |
| 4) | \( y=x^2+3x+4 \) | \( 3^2+3(3)+4 = 9+9+4 = 22 \) | \( 0^2+3(0)+4 = 4 \) | \( (-2)^2+3(-2)+4 = 4-6+4 = 2 \) |
| 5) | \( y=2x^2-x-7 \) | \( 2(3)^2-3-7 = 2(9)-3-7 = 18-3-7 = 8 \) | \( 2(0)^2-0-7 = -7 \) | \( 2(-2)^2-(-2)-7 = 2(4)+2-7 = 8+2-7 = 3 \) |
| 6) | \( y=-3x^2-x+20 \) | \( -3(3)^2-3+20 = -3(9)-3+20 = -27-3+20 = -10 \) | \( -3(0)^2-0+20 = 20 \) | \( -3(-2)^2-(-2)+20 = -3(4)+2+20 = -12+2+20 = 10 \) |
| 7) | \( y=\sqrt{3-x} \) | \( \sqrt{3-3} = \sqrt{0} = 0 \) | \( \sqrt{3-0} = \sqrt{3} \) | \( \sqrt{3-(-2)} = \sqrt{3+2} = \sqrt{5} \) |
| 8) | \( y=\sqrt{2x-5} \) | \( \sqrt{2(3)-5} = \sqrt{6-5} = \sqrt{1} = 1 \) | \( \sqrt{2(0)-5} = \sqrt{-5} \) (не определено) | \( \sqrt{2(-2)-5} = \sqrt{-4-5} = \sqrt{-9} \) (не определено) |
| 9) | \( y=-8\sqrt{-x+4} \) | \( -8\sqrt{-3+4} = -8\sqrt{1} = -8 \) | \( -8\sqrt{-0+4} = -8\sqrt{4} = -8(2) = -16 \) | \( -8\sqrt{-(-2)+4} = -8\sqrt{2+4} = -8\sqrt{6} \) |
| 10) | \( y=|x|+3 \) | \( |3|+3 = 3+3 = 6 \) | \( |0|+3 = 0+3 = 3 \) | \( |-2|+3 = 2+3 = 5 \) |
| 11) | \( y=|x|-8 \) | \( |3|-8 = 3-8 = -5 \) | \( |0|-8 = 0-8 = -8 \) | \( |-2|-8 = 2-8 = -6 \) |
| 12) | \( y=-|x| \) | \( -|3| = -3 \) | \( -|0| = 0 \) | \( -|-2| = -2 \) |
| 13) | \( y=|x+3| \) | \( |3+3| = |6| = 6 \) | \( |0+3| = |3| = 3 \) | \( |-2+3| = |1| = 1 \) |
| 14) | \( y=|x-5| \) | \( |3-5| = |-2| = 2 \) | \( |0-5| = |-5| = 5 \) | \( |-2-5| = |-7| = 7 \) |
Ответ: Заполненная таблица представлена выше.
