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.
- Identify the parent function \(f\).
- Describe the sequence of transformations from \(f\) to \(g\).
- Find the function \(g\).
- Use function notation to write \(g\) in terms of \(f\).
- Parent function: \(f(x)=x^2\)
- Transformations: Vertical shrink by 1/4 (or horizontal stretch by 2), Reflect over x-axis, Left 3, Up 4
- \(g(x)=-\dfrac{1}{4}(x+3)^2+4\)
- \(g(x)=-\dfrac{1}{4}f(x+3)+4\)
2. Consider the function \(g(x)=2\sqrt{-x+3}-4\).
- Identify the parent function \(f\).
- Describe the sequence of transformations from \(f\) to \(g\).
- Use function notation to write \(g\) in terms of \(f\).
- Parent function: \(f(x)=\sqrt{x}\)
- 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
- \(g(x)=2f(-x+3)-4\)