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Lesson: Transformations of Functions

Sample Question Videos

Worksheet • 25 Questions • 3 Videos

Q1:

Which function is represented below?

  • A 𝑔 ( 𝑥 ) = 𝑥 + 3
  • B 𝑔 ( 𝑥 ) = 𝑥 3
  • C 𝑔 ( 𝑥 ) = 𝑥 3
  • D 𝑔 ( 𝑥 ) = 𝑥 3
  • E 𝑔 ( 𝑥 ) = 𝑥 + 3

Q2:

The graph of function 𝑓 is produced from that of 𝑔 ( 𝑥 ) = 𝑥 by the following steps: a shift of 4 to the right, a dilation by a scale factor of 1 4 , and a shift of 4 up. What is the function 𝑓 ?

  • A 𝑓 ( 𝑥 ) = 𝑥 4 2 𝑥 + 8
  • B 𝑓 ( 𝑥 ) = 𝑥 4 2 𝑥
  • C 𝑓 ( 𝑥 ) = 𝑥 4 2 𝑥 + 5
  • D 𝑓 ( 𝑥 ) = 𝑥 4 + 2 𝑥 + 5
  • E 𝑓 ( 𝑥 ) = 𝑥 4 + 2 𝑥 + 8

Q3:

The following graph is a transformation of the graph of 𝑦 = | 𝑥 | . What is the function it represents? Write your answer in a form related to the transformation.

  • A 𝑦 = 4 | 𝑥 + 1 |
  • B 𝑦 = 4 | 𝑥 + 1 |
  • C 𝑦 = 4 | 𝑥 1 |
  • D 𝑦 = 4 | 𝑥 + 1 |
  • E 𝑦 = 4 + | 𝑥 + 1 |

Q4:

The function 𝑦 = 𝑓 ( 𝑥 ) is stretched in the horizontal direction by a scale factor of 1 2 . Write, in terms of 𝑓 ( 𝑥 ) , the equation of the transformed function.

  • A 𝑦 = 𝑓 ( 2 𝑥 )
  • B 𝑦 = 𝑓 ( 𝑥 2 )
  • C 𝑦 = 𝑓 ( 𝑥 + 2 )
  • D 𝑦 = 1 2 𝑓 ( 𝑥 )
  • E 𝑦 = 2 𝑓 ( 𝑥 )

Q5:

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

  • A ( 2 , 1 )
  • B ( 4 , 1 )
  • C ( 2 , 3 )
  • D ( 0 , 1 )
  • E ( 2 , 2 )

Q6:

Fares thinks that he can map the graph of the function to the graph of any other linear function by a translation followed by a stretch. This is equivalent to saying that any linear function can be written in the form for suitable values of and .

Is he right?

  • Ayes
  • Bno

Suppose that and is as before. Find and in terms of and when it is possible to write in the form .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Let and . Find the values of and for which . Use the following graph to help you.

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q7:

Graphs 𝐴 and 𝐵 in the diagram are the graphs of square root functions. They are symmetric about the origin. The equation of graph 𝐴 is 𝑦 = 1 3 𝑥 + 2 + 1 . Knowing that a point reflection about the origin is equivalent to a reflection in the 𝑥 -axis followed by a reflection in the 𝑦 -axis, find the equation of graph 𝐵 .

  • A 𝑦 = 1 3 𝑥 + 2 1
  • B 𝑦 = 1 3 𝑥 2 1
  • C 𝑦 = 1 3 𝑥 2 1
  • D 𝑦 = 1 3 𝑥 + 2 1
  • E 𝑦 = 1 3 𝑥 + 2 1

Q8:

Consider the function 𝑓 given by 𝑓 ( 𝑥 ) = 𝑥 + 1 2 .

Which of the graphs in the given diagram is the reflection of the graph of 𝑓 in the 𝑥 -axis?

  • AG
  • BF
  • CE
  • DH

Write its equation.

  • A 𝑦 = 𝑥 + 1 + 2
  • B 𝑦 = 𝑥 + 1 2
  • C 𝑦 = 𝑥 + 1 + 2
  • D 𝑦 = 𝑥 + 1 2

Q9:

Consider the function 𝑓 given by 𝑓 ( 𝑥 ) = 𝑥 + 1 + 2 .

Which of the graphs in the given diagram is the reflection of the graph of 𝑓 in the 𝑦 -axis?

  • AA
  • BE
  • CC
  • DG

Write its equation.

  • A 𝑦 = 𝑥 + 1 + 2
  • B 𝑦 = 𝑥 + 1 + 2
  • C 𝑦 = 𝑥 + 1 + 2
  • D 𝑦 = 𝑥 + 1 + 2

Q10:

Consider the function 𝑓 ( 𝑥 ) = 𝑥 1 + 2 .

Which of the following is the graph of 𝑦 = 𝑓 ( 𝑥 ) ?

  • AB
  • BA
  • CD
  • DC

State the domain and range of 𝑓 ( 𝑥 ) .

  • Adomain: 𝑥 1 , range: 𝑦 2
  • Bdomain: 𝑥 1 , range: 𝑦 2
  • Cdomain: 𝑥 1 , range: 𝑦 2
  • Ddomain: 𝑥 1 , range: 𝑦 2

Q11:

The figure shows the graph of 𝑦 = 𝑓 ( 𝑥 ) and the point 𝐴 . The point 𝐴 is a local maximum. Identify the corresponding local maximum for the transformation 𝑦 = 𝑓 ( 𝑥 1 ) + 4 .

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

Q12:

The red graph in the figure has equation 𝑦 = 𝑓 ( 𝑥 ) and the black graph has equation 𝑦 = 𝑔 ( 𝑥 ) . Express 𝑔 ( 𝑥 ) as a transformation of 𝑓 ( 𝑥 ) .

  • A 𝑔 ( 𝑥 ) = 2 𝑓 𝑥 2
  • B 𝑔 ( 𝑥 ) = 1 2 𝑓 𝑥 2
  • C 𝑔 ( 𝑥 ) = 1 2 𝑓 ( 2 𝑥 )
  • D 𝑔 ( 𝑥 ) = 2 𝑓 ( 𝑥 )
  • E 𝑔 ( 𝑥 ) = 𝑓 𝑥 2

Q13:

This is the graph of 𝑦 = 𝑔 ( 𝑥 ) .

Which of the following is the graph of 𝑔 ( 𝑥 ) ?

  • A(a)
  • B(b)
  • C(c)

Q14:

The figure shows the graph of 𝑦 = 𝑓 ( 𝑥 ) and point 𝐴 . Point 𝐴 is a local maximum. Identify the corresponding local maximum for the transformation 𝑦 = 𝑓 ( 𝑥 + 4 ) .