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Give an equation for the transformation that maps the graph of f onto the graph of g.

Give an equation for the transformation that maps the graph of f onto the graph of-example-1
User Alayna
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1 Answer

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Transformations of Graphs


g(x)=cf(b(x-h))+k

  • g(x) is the transformed function
  • f(x) is the original function
  • c = vertical stretch (negative = reflect about the x-axis)
  • b = horizontal stretch (negative = reflect about the y-axis)
  • h = horizontal translation (negative = moves left)
  • k = vertical translation (negative = moves down)

Solving the Question

We know that only a vertical translation and horizontal translation were applied to the graph. How?

  • The slopes of each segment remained the same, indicating that there was no vertical or horizontal stretch

To identify what values of h and k to use, identify the translations applied to one of the points:

(1,2) ⇒ (4,4)

  • It moved 3 units right
  • It moved 2 units up

Therefore:

  • h = 3
  • k = 2

Plug this into the equation:


g(x)=cf(b(x-h))+k\\g(x)=f(x-h)+k\\g(x)=f(x-3)+2

Answer


g(x)=f(x-3)+2

User Musk
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