Without the WP MathA font, the symbol (set of real numbers) appears as ú.
y = 4 x - 9 |
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x + 4y - 14 = 0 |
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(x - 2)2 + (y + 1)2 = 16 |
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x | x3 | y = x3 - x |
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0.0 | 0.000 | 0.000 |
0.5 | 0.125 | -0.375 |
1.0 | 1.000 | 0.000 | 1.5 | 3.375 | 1.875 | 2.0 | 8.000 | 6.000 |
f (x) is odd. |
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x intercepts occur where y = 0 :
y = x3 - x
=
x (x2 - 1)
=
x (x - 1) (x + 1)
y = 0
Þ
x = 0 or 1 or -1 .
y intercepts occur where x = 0 :
f (0) = 03 - 0 = 0
The x-intercepts are -1, 0, 1
and the only y-intercept is 0 . |
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The domain and range are both ú |
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2 + 3h + h2 , (h ¹ 0) |
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2 |
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3 x2 - 1 + 3xh + h2 |
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3 x2 - 1 |
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In general the domain is the set of all real numbers except those causing division by zero or the evaluation of an even root of a negative number.
We require
4x - 3 > 0
and
2x + 3 > 0
Þ
4x > 3
and
2x > -3
Þ
x > 3/4
and
x > -3/2
Þ
x > 3/4
At x = 3/4,
f (x) = 0 - Ö
(2(3/4) + 3)/2) =
- Ö(9/4) =
-3/2
We have a difference of two square roots, but the first root contains
the greater multiple of x and will dominate the second root.
The value of f (x) will increase indefinitely
from its starting value of -3/2.
The domain is [3/4, ¥) The range is [-3/2, ¥) |
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{ x | x ¹ -1 } |
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