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Worksheet: Horizontal and Vertical Stretches

Q1:

The figure shows the graph of 𝑦 = 𝑓 ( π‘₯ ) .

Which of the following is the graph of 𝑦 = 𝑓 ( 2 π‘₯ ) ?

  • A
  • B
  • C
  • D
  • E

Q2:

The figure shows the graph of 𝑦 = 𝑓 ( π‘₯ ) and the point 𝐴 . The point 𝐴 is a local maximum. Identify the corresponding local maximum for the transformation 𝑦 = 𝑓 ( π‘₯ ) 2 .

  • A ( 2 , 2 )
  • B ( 2 , 1 )
  • C ο€Ό 1 , 1 2 
  • D ο€Ό 2 , 1 2 
  • E ( 4 , 2 )

Q3:

The figure shows the graph of 𝑦 = 𝑓 ( π‘₯ ) .

Which of the following is the graph of 𝑦 = 2 𝑓 ( π‘₯ ) ?

  • A
  • B
  • C
  • D
  • E

Q4:

The figure shows the graph of 𝑦 = 𝑓 ( π‘₯ ) .

Which of the following is the graph of 𝑦 = 𝑓 ο€» π‘₯ 2  ?

  • A
  • B
  • C
  • D
  • E

Q5:

The red graph in the figure represents the equation 𝑦 = 𝑓 ( π‘₯ ) and the blue graph represents the equation 𝑦 = 𝑔 ( π‘₯ ) . Express 𝑔 ( π‘₯ ) as a transformation of 𝑓 ( π‘₯ ) .

  • A 𝑔 ( π‘₯ ) = 2 𝑓 ( π‘₯ )
  • B 𝑔 ( π‘₯ ) = 𝑓 ο€» π‘₯ 2 
  • C 𝑔 ( π‘₯ ) = 1 2 𝑓 ( π‘₯ )
  • D 𝑔 ( π‘₯ ) = 𝑓 ( 2 π‘₯ )
  • E 𝑔 ( π‘₯ ) = 1 2 𝑓 ( 2 π‘₯ )

Q6:

The figure shows the graph of 𝑦 = 𝑓 ( π‘₯ ) and the point 𝐴 . The point 𝐴 is a local maximum. Identify the corresponding local maximum for the transformation 𝑦 = 2 𝑓 ( π‘₯ ) .

  • A ( 4 , 1 )
  • B ( 2 , 1 )
  • C ( 4 , 2 )
  • D ( 2 , 2 )
  • E ο€Ό 2 , 1 2 

Q7:

The function 𝑦 = 𝑓 ( π‘₯ ) is stretched in the vertical direction by a scale factor of 1 2 . Write, in terms of 𝑓 ( π‘₯ ) , the equation of the transformed function.

  • A 𝑦 = 𝑓 ο€Ό 1 2 π‘₯ 
  • B 𝑦 = 2 𝑓 ( π‘₯ )
  • C 𝑦 = 𝑓 ( 2 π‘₯ )
  • D 𝑦 = 𝑓 ( π‘₯ ) 2
  • E 𝑦 = 𝑓 ( π‘₯ ) + 2

Q8:

The function 𝑦 = 𝑓 ( π‘₯ ) is stretched in the horizontal direction by a scale factor of 2. Write, in terms of 𝑓 ( π‘₯ ) , the equation of the transformed function.

  • A 𝑦 = 2 𝑓 ( π‘₯ )
  • B 𝑦 = 𝑓 ( 2 π‘₯ )
  • C 𝑦 = 𝑓 ( π‘₯ + 2 )
  • D 𝑦 = 𝑓 ο€» π‘₯ 2 
  • E 𝑦 = 1 2 𝑓 ( π‘₯ )

Q9:

The figure shows the graph of 𝑦 = 𝑓 ( π‘₯ ) and the point 𝐴 . The point 𝐴 is a local maximum. Identify the corresponding local maximum for the transformation 𝑦 = 𝑓 ( 2 π‘₯ ) .

  • A(4,2)
  • B(2,1)
  • C ο€Ό 1 , 1 2 
  • D(1,1)
  • E(4,1)

Q10:

The function 𝑦 = 𝑓 ( π‘₯ ) is stretched in the vertical direction by a scale factor of 2. Write, in terms of 𝑓 ( π‘₯ ) , the equation of the transformed function.

  • A 𝑦 = 𝑓 ( π‘₯ 2 )
  • B 𝑦 = 𝑓 ( 2 π‘₯ )
  • C 𝑦 = 1 2 𝑓 ( π‘₯ )
  • D 𝑦 = 2 𝑓 ( π‘₯ )
  • E 𝑔 ( π‘₯ ) = 1 2 𝑓 ( 2 π‘₯ )

Q11:

The figure shows the graph of 𝑦 = 𝑓 ( π‘₯ ) .

Which of the following is the graph of 𝑦 = 1 2 𝑓 ( π‘₯ ) ?

  • A
  • B
  • C
  • D
  • E

Q12:

The red graph in the figure represents the equation 𝑦 = 𝑓 ( π‘₯ ) and the purple graph represents the equation 𝑦 = 𝑔 ( π‘₯ ) . Express 𝑔 ( π‘₯ ) as a transformation of 𝑓 ( π‘₯ ) .

  • A 𝑔 ( π‘₯ ) = 𝑓 ο€» π‘₯ 2 
  • B 𝑔 ( π‘₯ ) = 2 𝑓 ( π‘₯ )
  • C 𝑔 ( π‘₯ ) = 1 2 𝑓 ( 2 π‘₯ )
  • D 𝑔 ( π‘₯ ) = 𝑓 ( π‘₯ ) 2

Q13:

The red graph in the figure represents the equation 𝑦 = 𝑓 ( π‘₯ ) and the orange graph represents the equation 𝑦 = 𝑔 ( π‘₯ ) . Express 𝑔 ( π‘₯ ) as a transformation of 𝑓 ( π‘₯ ) .

  • A 𝑔 ( π‘₯ ) = 𝑓 ( 2 π‘₯ )
  • B 𝑔 ( π‘₯ ) = 1 2 𝑓 ( π‘₯ )
  • C 𝑔 ( π‘₯ ) = 𝑓 ο€» π‘₯ 2 
  • D 𝑔 ( π‘₯ ) = 2 𝑓 ( π‘₯ )
  • E 𝑔 ( π‘₯ ) = 1 2 𝑓 ( 2 π‘₯ )

Q14:

The figure shows the graph of 𝑦 = 𝑓 ( π‘₯ ) and the point 𝐴 . The point 𝐴 is a local maximum. Identify the corresponding local maximum for the transformation 𝑦 = 𝑓 ο€» π‘₯ 2  .

  • A ο€Ό 1 , 1 2 
  • B ( 2 , 1 )
  • C ( 1 , 1 )
  • D ( 4 , 1 )
  • E ( 4 , 2 )

Q15:

The red graph in the figure represents the equation 𝑦 = 𝑓 ( π‘₯ ) and the green graph represents the equation 𝑦 = 𝑔 ( π‘₯ ) . Express 𝑔 ( π‘₯ ) as a transformation of 𝑓 ( π‘₯ ) .

  • A 𝑔 ( π‘₯ ) = 2 𝑓 ( π‘₯ )
  • B 𝑔 ( π‘₯ ) = 𝑓 ( 2 π‘₯ )
  • C 𝑔 ( π‘₯ ) = 1 2 𝑓 ( π‘₯ )
  • D 𝑔 ( π‘₯ ) = 𝑓 ο€» π‘₯ 2 
  • E 𝑔 ( π‘₯ ) = 1 2 𝑓 ( 2 π‘₯ )