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Functions, 2ADV F2 EQ-Bank 3 MC

The graph  \(y=\dfrac{2}{x-2}\)  undergoes the following transformations:

  • translated 3 units to the left
  • dilated vertically by a factor of 2

Determine which of the following is the new function.

  1.  \(2 y=\dfrac{2}{x+1}\)
  2.  \(\dfrac{y}{2}=\dfrac{2}{x-5}\)
  3.  \(2 y=\dfrac{2}{x-5}\)
  4.  \(\dfrac{y}{2}=\dfrac{2}{x+1}\)
Show Answers Only

\(\Rightarrow D\)

Show Worked Solution

\(\text{Translate 3 units to the left:}\)

\(y=\dfrac{2}{x-2} \ \Rightarrow \ y^{′}=\dfrac{2}{(x+3)-2}=\dfrac{2}{x+1}\)
 

\(\text{Dilate vertically by a factor of 2:}\)

\(y^{′}=\dfrac{2}{x+1} \ \Rightarrow \ \dfrac{y^{″}}{2}=\dfrac{2}{x+1}\)

\(\Rightarrow D\)