Instructions
In this worksheet, you will explore how linear functions can be transformed on a graph. For each transformation described, sketch the graph of the original function, apply the transformations, and then describe the effects of those transformations. Use the grid provided for your sketches.
Part 1: Understanding the Basic Linear Function
The basic linear function is given by the equation y = 2x + 1.
a) Sketch the graph of the basic linear function.
What is the slope and y-intercept of this function?
Slope: _______________
Y-intercept: _______________
Part 2: Applying Transformations
b) Now, consider the transformation y = 2x + 3. What effect does this transformation have on the graph compared to the original function?
Describe the transformation: _____________________________________________________________
c) Next, look at the function y = -2x + 1. What transformation is applied here compared to the original function?
Describe the transformation: _____________________________________________________________
d) Now, analyze the function y = 2(x - 1) + 1. How does this transformation affect the graph?
Describe the transformation: _____________________________________________________________
Part 3: Reflection and Summary
List the different types of transformations you have explored:
- Vertical Shift: ________________________________________________________
- Horizontal Shift: ______________________________________________________
- Reflection: _____________________________________________________________
- Stretch/Compression: ___________________________________________________
Which transformation did you find most interesting and why?
Your response: ______________________________________________________________________