Worksheet: Transformations of a Square Root Function

In this worksheet, we will practice graphing composite transformations of square root functions, choosing the right graph that fits the given function, and stating their domain and range after these transformations.

Q1:

Consider the function 𝑔 ( 𝑥 ) that has been obtained by dilating 𝑓 ( 𝑥 ) = 𝑥 + 4 in the horizontal direction by a factor of 1 2 .

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

  • A 𝐴
  • B 𝐷
  • C 𝐶
  • D 𝐵

What is the equation of 𝑔 ( 𝑥 ) ?

  • A 𝑔 ( 𝑥 ) = 1 2 𝑥 + 4
  • B 𝑔 ( 𝑥 ) = 𝑥 2 + 4
  • C 𝑔 ( 𝑥 ) = 2 𝑥 + 4
  • D 𝑔 ( 𝑥 ) = 2 𝑥 + 4

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