Valupatitta
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Can some1 pls explain how to do adding/subtracting/multiplying curves please??? cos im really lost :S
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Curve Sketching Help! (1 Viewer)
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In adding and subtracting functions just remember.Valupatitta said:
In addition you just add the sub-ordinates of both functions and get a rough outline of the functions whilst still considering asymptotes and limits.
In subtraction you just subtract each ordinate in both respective graphs but consider limits and asymptotes.
In the multiplication of functions it is better to just consider the basic properties of the functions and use calculus to determine gradients turning points and consider asymptotes.
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Basically look for certain key points such as those intercepting the x-axis, minimum and maximum values and like previous comment any limits and asymptotes. So if one graph has an x-axis intercept then you know for addition the value at that point lies in the other graph and for multiplication it will lies in the x-axis....actually i dont think you can really explain it just go and look at worked examples and you can easily learn from them
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For addition and subtraction, it's mainly manually adding and subtracting ordinates (y-values). Once you can work out where the addition/subtraction of two ordinates lie, you should notice a pattern at certain regions of the curve and can join the dots to figure out the curve.
For example, y = x + sin x, you start with a typical y = sin x curve. For small positive x, you shift the y coordinates of sin x up by a small value of x and for large positive x, this shift upwards is greater (resulting in a 'slanted' shift upwards). This is similarly the case for small and large negative x, where the shift is downwards instead. After this, you end up with a "slanted" sine curve.
For multiplication y= f(x)g(x), the most useful technique is to note what the sign of the ordinate is after multiplication. If you have two curves that have the same sign in y-value for a given x-value, then the resultant ordinate is positive. (i.e. f(x) > 0 and g(x) > 0 OR f(x) < 0 and g(x) < 0, then f(x)g(x) > 0)
If you have two curves that have the opposite sign in y-value for a given x-value, then the resultant ordinate is negative. (i.e. f(x) > 0 and g(x) < 0 OR f(x) < 0 and g(x) > 0, then f(x)g(x) < 0)
If one of the curves has an x-intercept (y = 0), then when you mutliply it by any defined ordinate, the result is still y = 0, so the x-intercept is conserved.
The rest is by inspection.
For example, y = x + sin x, you start with a typical y = sin x curve. For small positive x, you shift the y coordinates of sin x up by a small value of x and for large positive x, this shift upwards is greater (resulting in a 'slanted' shift upwards). This is similarly the case for small and large negative x, where the shift is downwards instead. After this, you end up with a "slanted" sine curve.
For multiplication y= f(x)g(x), the most useful technique is to note what the sign of the ordinate is after multiplication. If you have two curves that have the same sign in y-value for a given x-value, then the resultant ordinate is positive. (i.e. f(x) > 0 and g(x) > 0 OR f(x) < 0 and g(x) < 0, then f(x)g(x) > 0)
If you have two curves that have the opposite sign in y-value for a given x-value, then the resultant ordinate is negative. (i.e. f(x) > 0 and g(x) < 0 OR f(x) < 0 and g(x) > 0, then f(x)g(x) < 0)
If one of the curves has an x-intercept (y = 0), then when you mutliply it by any defined ordinate, the result is still y = 0, so the x-intercept is conserved.
The rest is by inspection.