text: # The graph of the function g is formed by applying the indicated sequence of transformation to the given function f. Find the function g: a) The graph of f(x)= absolute value of x is reflected about...
  
  The graph of the function g is formed by applying the indicated sequence of transformation to the given function f. Find the function g:
  
  a) The graph of f(x)= absolute value of x is reflected about the x-axis, vertically shrunk by a factor of .5, shifted 3 units to the right and shifted 2 units down.
  
  b) The graph of f(x)= cube root of x is shifted four units to the left and two units down. For this one I got f(x)= (cube root of x +4) -2 .. is that correct?
  
  Asked on by ceeee
  
  rcmath | High School Teacher | (Level 1) Associate Educator
  
  Posted on
  
  A) When you reflect abs(x) about the x-axis, you end up with -abs(x).
  
  Next let's pay attention to the fact that when yo multiply by 0.5 the graph actually expand and not shrink. So for it to shrink by half means to multiply by 2.
  Shift to the right 3 means subtract 3 from x, and 2 up, you add 2 to the function. Thus we end up with
  
  `y=2lx-3l+2` (that is 2*abs(x-3)+2)
explanation: The text extract contains a math question and an answer to one of the parts of the question. It describes a problem where the user is asked to find the function \( g \) after applying a sequence of transformations to a given function \( f \). The user provides an answer for part (b) of the question, and the teacher confirms the correctness of the answer.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # The graph of the function g is formed by applying the indicated sequence of transformation to the given function f. Find the function g: a) The graph of f(x)= absolute value of x is reflected about...
  
  The graph of the function g is formed by applying the indicated sequence of transformation to the given function f. Find the function g:
  
  a) The graph of f(x)= absolute value of x is reflected about the x-axis, vertically shrunk by a factor of .5, shifted 3 units to the right and shifted 2 units down.
  
  b) The graph of f(x)= cube root of x is shifted four units to the left and two units down. For this one I got f(x)= (cube root of x +4) -2 .. is that correct?
  
  Asked on by ceeee
  
  rcmath | High School Teacher | (Level 1) Associate Educator
  
  Posted on
  
  A) When you reflect abs(x) about the x-axis, you end up with -abs(x).
  
  Next let's pay attention to the fact that when yo multiply by 0.5 the graph actually expand and not shrink. So for it to shrink by half means to multiply by 2.
  Shift to the right 3 means subtract 3 from x, and 2 up, you add 2 to the function. Thus we end up with
  
  `y=2lx-3l+2` (that is 2*abs(x-3)+2)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The text extract contains a math question and an answer to one of the parts of the question. It describes a problem where the user is asked to find the function \( g \) after applying a sequence of transformations to a given function \( f \). The user provides an answer for part (b) of the question, and the teacher confirms the correctness of the answer.
  
  Label: question-and-answer