For Mathguru

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Math 30-1: Unit 2 Transformations Assignment

Name: _____________________________ /22 Marks

If your name does not appear in your writing on the hardcopy scan – you will lose one mark!

SHOW ALL WORK!!

1. Write an equation to represent each translation of the function y = |x|.

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2. For y = f (x) as shown, graph the following.

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3. The key point (12, −5) is on the graph of y = f (x). Determine the coordinates of its image point under

each transformation.

a) /1 b) /1

4. If the range of function y  f (x) is {y  y  4}, state the range of the new function g(x)  f (x  2)  3.

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5. As a result of the transformation of the graph of y  f (x) into the graph of y  3f (x  2)  5, the point (2, 5) becomes point (x, y). Determine the value of (x, y). (SHOW WORK)

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6. The graph of f (x) is stretched horizontally by a factor of 1

2 about the y-axis and then stretched

vertically by a factor of about the x-axis. Determine the equation of the transformed function.

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7.A function f (x)  x2  x  2 is multiplied by a constant value k to create a new function g(x)  k f (x). If

the graph of y  g(x) passes through the point (3, 14), state the value of k. (show work)

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8. The graph of the function y = f (x) is given. Graph each of the following transformations of

the function. Show each stage of the transformation in a different colour.

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3

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9. Determine algebraically the inverse of each function. If necessary, restrict the domain so that the

inverse of f(x) is also a function. Verify by sketching the graph of the function and its inverse.

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10. One the same grid, sketch the graph of the inverse relation.

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11. The graphs of y  f (x) and y  g(x) are shown.

a) If the point (1, 1) on y  f (x) maps onto the point (1, 2) on y  g (x), describe the transformation and state the equation of g (x).

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b) If the point (4, 2) on y  f (x) maps onto the point (1, 2) on y  g (x), describe the transformation and state the equation of g (x).

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12.

Consider the graph of the function y  f (x).

a) Describe the transformation of y  f (x) to y  3f (2 (x  1))  4.

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b) Sketch the graph on the same grid above.

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13. A function is defined by f (x)  (x  2)(x  3).

a) If g(x)  kf (x), describe how k affects the y-intercept of the graph of the function y  g(x)

compared to y  f (x).

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c) If h(x)  f (mx), describe how m affects the x-intercepts of the graph of the function y

 h(x) compared to y  f (x).

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