Transforming Linear Functions Practice Worksheet for 13-Year-Olds | Algebra 1

Instructions

Complete the following exercises on transforming linear functions. Show all your work where applicable.

1. Understanding Transformations

Define the following transformations that can be applied to the linear function f(x) = x:

• a. Vertical shift up by 3: f(x) = ____________________
• b. Vertical shift down by 5: f(x) = ____________________
• c. Horizontal shift to the right by 2: f(x) = ____________________
• d. Horizontal shift to the left by 4: f(x) = ____________________

2. Identifying Transformations

For each of the following functions, describe how the function has been transformed from f(x) = x:

• a. g(x) = x + 4:

Transformation: ____________________

• b. h(x) = 2x - 1:

Transformation: ____________________

• c. j(x) = -x + 6:

Transformation: ____________________

• d. k(x) = (x - 3) / 2:

Transformation: ____________________

3. Creating Your Functions

Create your own transformations of the function f(x) = x and write the new function:

• a. Vertical shift up by 7: New Function: ____________________
• b. Reflect over the x-axis: New Function: ____________________
• c. Horizontal shift left by 1 and vertical shift down by 2: New Function: ____________________

4. Analyzing Graphs

Consider the following functions:

• m(x) = -3(x + 2) + 1
• n(x) = (1/2)x - 4

Sketch the parent function f(x) = x and each of the transformed functions on a coordinate plane below. Mark the points of intersection, if any.

1. Sketch of f(x) = x:

 
    |
  5 |         *
  4 |
  3 |
  2 |    *
  1 |
----|----------------- 
 -2 | *
 -3 |   
 -4 |   
 -5 |  

2. Sketch of m(x):

    |
  5 |          
  4 |   
  3 |          
  2 |          
  1 |   *
----|----------------- 
 -2 |          *    
 -3 |   
 -4 |   *
 -5 |    

3. Sketch of n(x):

    |
  5 |          
  4 |       
  3 |         
  2 |          
  1 |          
----|----------------- 
 -2 |       *  
 -3 |       
 -4 |  * 
 -5 |   

5. Reflection Questions

Answer the following questions:

• a. What changes occurred to the function when reflecting over the x-axis?

Answer: _______________________________________________

• b. How do vertical shifts affect the position of the graph?

Answer: _______________________________________________

• c. Why is understanding transformations important in algebra?

Answer: _______________________________________________

Review your answers and make sure to ask questions if you're unsure about any transformation concepts!