Let f(x)=8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down. What is an equation for g(x)?

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Noah G Share
Mar 7, 2017

Answer:

#g(x) = 32x - 7#

Explanation:

In #y = afb(x + c) + d#:

#a# represents the vertical stretch

#b# represents the horizontal stretch

#c# represents the horizontal translation

#d# represents the vertical translation

We are given that #g(x)# has a vertical stretch and a vertical translation (down and up are on the y-axis, hence it's a vertical translation).

Therefore, the equation of #g(x)# is

#g(x) = 4(8x) - 7 =32x - 7#

Practice Exercises

  1. Consider the function #f(x) = x^3#. #f(x)# undergoes a vertical transformation of #5# units down and a horizontal translation of #2# units right. It is reflected over the x-axis. What is #f(x)#'s new equation?

  2. The point #(6, -4)# lies on the graph of function #g(x)#. What are the coordinates of the point that will lie on #2g(3x - 9) + 1#?

Solutions

  1. #f(x) = -(x - 2)^3 + 2#
  2. #(5, -7)#

Hopefully this helps!

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