Shifting functions introduction | Transformations of functions | Algebra 2 | Khan Academy

TL;DR

Learn how to shift functions up, down, left, and right using the Desmos online graphing calculator.

Transcript

• [Instructor] So I am here at desmos.com, which is an online graphing calculator, and the goal of this video is to explore how shifts in functions happen. How do things shift to the right or left or how do they shift up and down? And what we're going to start off doing is just graph a plain vanilla function, f of x is equal to x squared. That look... Read More

Key Insights

• 🪜 Adding or subtracting a constant value shifts a function vertically.
• 👉 Replacing the x variable with x minus a value shifts the function to the right.
• 👈 Replacing the x variable with x plus a value shifts the function to the left.
• 🎚️ Sliders can be used to easily adjust and visualize shifts in a function.
• ☺️ The shifting principles can be applied to various functions, not just the core x squared function.
• 🉐 Exploring different functions with the Desmos graphing calculator helps in gaining an intuition about function shifts.
• 💱 Shifting a function vertically changes the y value, while shifting horizontally changes the x value.

Questions & Answers

Q: How can a function be shifted up or down?

To shift a function up, add a constant value to the function. Conversely, subtracting a value will shift the function down. This changes the y value of the function, resulting in a vertical shift.

Q: How can a function be shifted to the left or right?

To shift a function to the left, replace the x variable with x minus a value. This effectively moves the entire graph to the right. On the other hand, substituting x with x plus a value shifts the function to the left.

Q: Can these shifts be generalized and visualized?

Yes, by adding sliders for different variables, such as k and h, the shifts can be easily adjusted and visualized on the graph. Increasing or decreasing the slider values will result in corresponding shifts in the function.

Q: Can these shifting principles be applied to other functions?

Yes, the principles of shifting can be applied to various functions, including absolute value functions. By replacing x with x plus or minus a value, different shifts can be achieved, allowing for further exploration and intuitive understanding.

Summary & Key Takeaways

• The video demonstrates how to shift functions up or down by adding or subtracting a constant value.

• When the x variable is replaced with x minus a value, the function shifts to the right.

• By adding sliders for different variables, the video shows how to generalize and visualize these shifts.