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Identifying Graphs - Families of curves

Identifying Graphs - Families of curves. Algebra. Looking at families of curves . In this unit we will look at five different families of curves. The family of curves y = kx , represent a set of straight lines passing through the origin.

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Identifying Graphs - Families of curves

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  1. Identifying Graphs -Families of curves Algebra

  2. Looking at families of curves. In this unit we will look at five different families of curves. • The family of curves y = kx , represent a set of straight lines passing • through the origin. • Use your graphic calculator to look at this family of curves for • different values of k. Use k = 1 , 2 , 3 , 4 , 0.5 , 0.25 etc. • Also consider the case when k is negative by looking • at k = -1 , -2 , -3 , -4 , -0.5 , etc. • Window = [ -8 , 8 , 1 , -8 , 8 , 1 , 1 ] 2. The family of curves y = kx2 represents a family of parabolas. Use your calculator to draw the curves when k = 1 , 2 , 3 , 4 , 0.5 , 0.25 etc Window = [ -4 , 4 , 1 , -2 , 16 , 2 , 1 ]

  3. 3. Use your calculator to study the family of curves y = kx3. Look at the cases when k = 1 , 2 , 3 , 0.8 , 0.5 , 0.25 etc Window = [ -4 , 4 , 1 , -20 , 20 , 5 , 1 ] 4. Use your calculator to study the family of curves y = k√x. This is a family of curves which you might not be familiar with and may not have seen before. Look at the shape of the curves which make up the family by drawing them for k = 1 , 2 , 3 , 4 , 0.8 , 0.5 etc Window = [ -1 , 5 , 1 , -1 , 6 , 1 , 1 ] 5. Consider the family of curves represented by the equation . Use your calculator to draw the curves when k = 1 , 2 , 5 , 10 , 20 , etc Window = [ -2 , 8 , 1 , -2 , 8 , 1 , 1 ]

  4. y  (4,6) 0 x You should now be able to identify a curve as belonging to one of the five families above, and if you are given a point on the curve then you should be able to find the equation of the curve. The example below illustrates this idea.

  5. Examples. y (5,3)  y 0  (3,8) x 0 x y y  (2,16)  (2,5) y  (16,20) 0 x 0 x 0 x Try to identify the family and hence find the equation of the curve in the examples which follows

  6. y (2,7.5)  (5,5) y 0 x 0 x y  y (-3,4)  (5,4) 0 x 0 x y y (-8,5)  0 x (-2,-1) 0  x Try to identify the family and hence find the equation of the curve in the examples which follows

  7. y (-12,3)  x 0 y (2.5,2.5)  0 x y  (3,3) 0 x y y (5,5)   (8,3) 0 0 x x y (6,14)  0 x Try to identify the family and hence find the equation of the curve in the examples which follows

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