# Section 1.6&7 – Parent Functions and Transformations

Section Details.
• 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

### Practice Problems

Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it.

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. $$g(x)=-\dfrac{1}{4}f(x+3)+4$$

To see the full video page and find related videos, click the following link.

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

To see the full video page and find related videos, click the following link.