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Worksheet: Graphing Transformations of Exponential Functions

Q1:

Which of the following expressions does NOT describe the shown graph?

  • A 𝑁 = 8 0 β‹… 𝑒 l n 1 . 2 5 β‹… 𝑑
  • B 𝑁 = 8 0 β‹… 1 . 2 5 𝑑
  • C 𝑁 = 8 0 β‹… 2 l n l n 1 . 2 5 2 𝑑
  • D 𝑁 = 8 0 β‹… 2 l n l n 2 1 . 2 5 𝑑
  • E 𝑁 = 8 0 β‹… ο€½ 2  l n l n 1 . 2 5 2 𝑑

Q2:

Which of the following expressions does NOT describe the shown graph?

  • A 𝑁 = 1 5 β‹… 2 𝑑 2 . 4
  • B 𝑁 = 1 5 β‹… ο€Ό 4 3  𝑑
  • C 𝑁 = 1 5 β‹… 𝑒 0 . 2 8 8 𝑑
  • D 𝑁 = 1 5 β‹… 2 2 . 4 𝑑
  • E 𝑁 = 1 5 β‹… ο€Ό 3 4  βˆ’ 𝑑

Q3:

William has graphed three exponential functions all in the form 𝑦 = π‘Ž 𝑒 𝑏 π‘₯ or 𝑦 = π‘Ž 𝑒 1 𝑏 π‘₯ where π‘Ž and 𝑏 are positive integers.

The red graph is 𝑦 = 𝑒 π‘₯ .

By considering properties of graphical transformations, determine the equation of the blue graph.

  • A 𝑦 = 2 𝑒 2 π‘₯
  • B 𝑦 = 𝑒 1 2 π‘₯
  • C 𝑦 = 1 2 𝑒 2 π‘₯
  • D 𝑦 = 𝑒 2 π‘₯
  • E 𝑦 = 2 𝑒 1 2 π‘₯

By considering properties of graphical transformations, determine the equation of the green graph.

  • A 𝑦 = 𝑒 1 2 π‘₯
  • B 𝑦 = 2 𝑒 1 2 π‘₯
  • C 𝑦 = 1 2 𝑒 1 2 π‘₯
  • D 𝑦 = 𝑒 2 π‘₯
  • E 𝑦 = 1 2 𝑒 2 π‘₯

Q4:

William has graphed three exponential functions all in the form 𝑦 = π‘Ž 𝑒 π‘₯ .

The red graph represents the equation 𝑦 = 𝑒 π‘₯ .

By considering properties of graphical transformations, determine the equation of the blue graph.

  • A 𝑦 = 1 2 𝑒 π‘₯
  • B 𝑦 = 2 𝑒 π‘₯
  • C 𝑦 = 𝑒 π‘₯ βˆ’ 0 . 5
  • D 𝑦 = 3 𝑒 π‘₯
  • E 𝑦 = 𝑒 π‘₯ βˆ’ 1

By considering properties of graphical transformations, determine the equation of the green graph.

  • A 𝑦 = 1 2 𝑒 π‘₯
  • B 𝑦 = 1 2 𝑒 π‘₯ βˆ’ 0 . 5
  • C 𝑦 = 7 1 0 𝑒 π‘₯ βˆ’ 0 . 5
  • D 𝑦 = 𝑒 π‘₯ βˆ’ 0 . 5
  • E 𝑦 = 1 4 𝑒 π‘₯

Q5:

Which of the following translations will move the curve 𝑦 = 𝑒 + 9 π‘₯ βˆ’ 6 to the curve 𝑦 = 𝑒 π‘₯ ?

  • A ( βˆ’ 6 , βˆ’ 9 )
  • B ( βˆ’ 6 , 9 )
  • C ( 9 , 6 )
  • D ( 6 , 9 )

Q6:

This is the graph of the exponential function 𝑦 = 𝑓 ( π‘₯ ) .

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

  • A(c)
  • B(a)
  • C(b)