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Worksheet: Periodic Graphs Transformation

Q1:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to 𝑓 ( 2 π‘₯ ) . Determine the coordinates of 𝐴 following this transformation.

  • A ( 1 8 0 , βˆ’ 0 . 5 )
  • B ( 3 6 0 , βˆ’ 1 )
  • C ( 1 8 0 , βˆ’ 2 )
  • D ( 9 0 , βˆ’ 1 )
  • E ( 9 0 , βˆ’ 0 . 5 )

Q2:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to 𝑓 ( π‘₯ ) βˆ’ 3 . Determine the coordinates of 𝐴 following this transformation.

  • A ( 4 2 , βˆ’ 2 )
  • B ( 4 5 , 4 )
  • C ( 4 8 , 1 )
  • D ( 4 5 , βˆ’ 2 )
  • E ( 4 2 , 1 )

Q3:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to 𝑓 ( π‘₯ + 4 5 ) . Determine the coordinates of 𝐴 following this transformation.

  • A ( 9 0 , βˆ’ 4 4 )
  • B(135, 1)
  • C ( 4 5 , βˆ’ 4 4 )
  • D(45, 1)
  • E(90, 46)

Q4:

The figure shows the graph of . A transformation maps to . Determine the coordinates of following this transformation.

  • A
  • B
  • C
  • D
  • E

Q5:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to 𝑓 ( 2 π‘₯ ) . Determine the coordinates of 𝐴 following this transformation.

  • A ( 4 5 , 2 )
  • B ( 9 0 , 1 )
  • C ( 4 5 , 0 . 5 )
  • D ( 2 2 . 5 , 1 )
  • E ( 2 2 . 5 , 0 . 5 )

Q6:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to βˆ’ 3 𝑓 ( 5 π‘₯ βˆ’ 5 ) βˆ’ 4 . Determine the coordinates of 𝐴 following this transformation.

  • A ( 1 0 , βˆ’ 3 )
  • B ( 1 4 , βˆ’ 7 )
  • C ( 1 4 , βˆ’ 3 )
  • D ( 1 0 , βˆ’ 7 )
  • E ( 1 4 , βˆ’ 4 )

Q7:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to 𝑓 ( 2 π‘₯ ) . Determine the coordinates of 𝐴 following this transformation.

  • A (90, 0.5)
  • B (180, 1)
  • C (90, 2)
  • D (45, 1)
  • E (45, 0.5)

Q8:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to 𝑓 ( π‘₯ βˆ’ 4 5 ) . Determine the coordinates of 𝐴 following this transformation.

  • A ( 1 8 0 , βˆ’ 4 6 )
  • B ( 1 3 5 , βˆ’ 1 )
  • C ( 1 8 0 , 4 4 )
  • D ( 2 2 5 , βˆ’ 1 )
  • E ( 2 2 5 , 4 4 )

Q9:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to βˆ’ 4 𝑓 ( π‘₯ ) . Determine the coordinates of 𝐴 following this transformation.

  • A ( βˆ’ 1 8 0 , 1 )
  • B ( 4 5 , βˆ’ 0 . 2 5 )
  • C ( βˆ’ 1 1 . 2 5 , 1 )
  • D ( 4 5 , βˆ’ 4 )
  • E ( βˆ’ 1 8 0 , βˆ’ 4 )

Q10:

On the left is the graph of 𝑓 ( π‘₯ ) and on the right is the graph of 𝐴 𝑓 ( π‘₯ ) + 𝐡 for some numbers 𝐴 and 𝐡 .

What is the pair ( 𝐴 , 𝐡 ) ?

  • A ( 0 , βˆ’ 3 )
  • BThey cannot be determined.
  • C ( βˆ’ 2 , 3 )
  • D ( 2 , βˆ’ 3 )
  • E ( 0 , 3 )

Q11:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to 2 𝑓 ( π‘₯ ) . Determine the coordinates of 𝐴 following this transformation.

  • A (45, 1)
  • B (90, 0.5)
  • C (180, 1)
  • D (90, 2)
  • E (45, 0.5)

Q12:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to 𝑓 ( π‘₯ ) + 2 . Determine the coordinates of 𝐴 following this transformation.

  • A (92, 1)
  • B ( 9 0 , βˆ’ 1 )
  • C (92, 3)
  • D (90, 3)
  • E (88, 1)

Q13:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to 2 𝑓 ( π‘₯ ) . Determine the coordinates of 𝐴 following this transformation.

  • A ( 9 0 , βˆ’ 1 )
  • B ( 1 8 0 , βˆ’ 0 . 5 )
  • C ( 3 6 0 , βˆ’ 1 )
  • D ( 1 8 0 , βˆ’ 2 )
  • E ( 3 6 0 , βˆ’ 2 )

Q14:

The figure shows the graph of 𝑓 ( π‘₯ ) . A transformation maps 𝑓 ( π‘₯ ) to 3 𝑓 ( 2 π‘₯ βˆ’ 9 0 ) + 1 . Determine the coordinates of 𝐴 following this transformation.

  • A (90, 3)
  • B (135, 4)
  • C (135, 3)
  • D (90, 4)
  • E (90, 2)