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Virtual Math Learning Center

Virtual Math Learning Center Texas A&M University Virtual Math Learning Center

Section 1.6&7 – Parent Functions and Transformations

  • Learning the properties and graphs for a catalog of standard functions 
  • Vertical and horizontal shifts of functions
  • Reflections of functions about the x-axis and y-axis
  • Vertical stretches and shrinks of functions
  • Horizontal stretches and shrinks of functions
  • Learning the order to apply the transformations 
  • Using the parent function and transformations to graph a function
  • Writing the function for graph by identifying the parent function and all transformations

Exercises

Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.

1. The graph of a function \(g\) is given below.

  1. Identify the parent function \(f\).
  2. Describe the sequence of transformations from \(f\) to \(g\).
  3. Find the function \(g\).
  4. Use function notation to write \(g\) in terms of \(f\).

  1. Parent function: \(f(x)=x^2\)
  2. Transformations: Vertical shrink by 1/4 (or horizontal stretch by 2), Reflect over x-axis, Left 3, Up 4
  3. \(g(x)=-\dfrac{1}{4}(x+3)^2+4\)
  4. \(g(x)=-\dfrac{1}{4}f(x+3)+4\)

If you would like to see more videos on this topic, click the following link and check the related videos.

2. Consider the function \(g(x)=2\sqrt{-x+3}-4\).​

  1. Identify the parent function \(f\).
  2. Describe the sequence of transformations from \(f\) to \(g\).
  3. Use function notation to write \(g\) in terms of \(f\).

  1. Parent function: \(f(x)=\sqrt{x}\)
  2. Transformations: Reflect over \(y\)-axis, Right 3, Vertical stretch by 2, Down 4 OR Left 3, Reflect over \(y\)-axis, Vertical stretch by 2, Down 4
  3. \(g(x)=2f(-x+3)-4\)

If you would like to see more videos on this topic, click the following link and check the related videos.