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  7.  y = f(x +2) -7

  8.  y = -f(x -5)

  9.  y = f(-x) +3

Step-by-step explanation:

The general transformation can be written ...

  y = a·f(b·(x -c)) +d

'a' is the vertical expansion factor. A negative value means the graph is reflected over the x-axis.

'b' is the horizontal compression factor. A negative value means the graph is reflected over the y-axis.

'c' is the number of units of right-shift.

'd' is the number of units of up-shift.

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7. 2 left and 7 down means (c, d) = (-2, -7), so the transformed function is ...

  y = f(x +2) -7

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8. reflected over x and 5 right means (a, c) = (-1, 5), so the transformed function is ...

  y = -f(x -5)

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9. reflected over y and up 3 means (b, d) = (-1, 3), so the transformed function is ...

  y = f(-x) +3

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The graph shows an asymmetrical function that makes it possible to tell what the transformations are. The original is dashed orange. The various y-values correspond to the problem numbers. You can see that the transformations match the problem statements.

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step-by-step explanation: