Translation of Functions (part1): shift the graph in 4 directions

TL;DR

Learn how to shift a function's graph up, down, left, and right, and write equations to represent these shifts.

Transcript

let's talk about how we can shift the graph of a function to the up direction to the right direction and the down Direction and of course the left directions so here we are given this function f ofx equal to x² we are going to see and pay attention to how to write an equation that will associate this shift Ms these four directions okay so notice th... Read More

Key Insights

• ❣️ The x-value in the equation determines the horizontal position of the vertex, while the y-value determines the vertical position.
• 👉 Shifting the graph to the right involves adding a number to the x-value in the equation.
• 👈 The opposite is true for shifting to the left, as this requires subtracting a number from the x-value.
• #️⃣ Adding a number to the y-value in the equation shifts the graph upward, while subtracting a number shifts it downward.
• 🗯️ The equation for shifting right is written as f(x - 2), while shifting left is f(x + 2).
• 📈 Shifting the graph upward is represented by f(x) + 1, and downward by f(x) - 1.
• 😑 Understanding these equations allows for accurately translating graph shifts into mathematical expressions.

Questions & Answers

Q: How can the graph of a function be shifted to the right?

To shift the graph of a function to the right, add the desired number directly to the x-value in the equation. For example, if you want to shift the graph two units to the right, make the x-value in the equation x - 2.

Q: What is the equation for shifting a function to the left?

To shift the graph of a function to the left, subtract the desired number from the x-value in the equation. For instance, if you want to shift the graph two units to the left, the equation would be x + 2.

Q: How can the graph of a function be shifted upward?

To shift the graph of a function upward, add the desired number to the y-value in the equation. This means placing the number after the x-value squared. For example, if you want to shift the graph one unit upward, the equation would be x^2 + 1.

Q: What is the equation for shifting a function downward?

To shift the graph of a function downward, subtract the desired number from the y-value in the equation. Similarly to shifting upward, place the number after the x-value squared. For instance, if you want to shift the graph one unit downward, the equation would be x^2 - 1.

Summary & Key Takeaways

• A function with a vertex at (0,0) can be shifted right by adding a number directly to the x-value in the equation.

• To shift the graph left, subtract the desired number from the x-value in the equation.

• Shifting the graph up involves adding a number to the y-value in the equation, while shifting down requires subtracting a number from the y-value.