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SOMETHINGS' MATHEMATICAL,     TOO


TRANSFORMATIONS  Worksheet

 Name :

For each of the following questions: answer the question and draw the graphs.

1. Graph the functions, f (x) = x3 +1, g (x) = x3 - 5, h (x) = (- x)3 + 4. Compare these graphs to their toolkit function, k (x) = x3. Describe the transformations on k (x) that would result in f, g and h.

2. Graph the functions, f (x) = (x + 1) 3 , g (x) = - (x - 5)3 , h (x) = (x + 4)3 . Compare these graphs to their toolkit function, k (x) = x3. Describe the transformations on k (x) that would result in f, g and h.

3. Graph the functions, f (x) = abs (x)  + 5,  g (x) = 1/ (x + 2),  h (x) = - abs(x + 3) - 3. Compare these graphs to their toolkit functions, k (x). Describe the transformations on k(x) that would result in f, g and h.

4. If k (x) = x write the transformations required to obtain f(x) = 0.5 abs(x - 1) - 4

For 5 - 9, if k (x) = 3x - 2 write the expression for g (x) if the graph of g is obtained by:

5. A reflection across the y axis                               6. A reflection across the x axis

7. A vertical translation of +3 units                           8. A horizontal translation of - 3 units

9. A vertical stretch of 3 units

10. For the graph of k (x) below, sketch the graph that corresponds to the following transformations:

      

transformgraph
 

                   a) y = k (x + 3)                         b) y = 2 k (x) + 3

                   c) y = - 2 k (x)                         d) y = k (- x + 1) - 1


Algebra/Calculus

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