Introduction to Horizontal and Vertical Transformations of Graphs

TL;DR

This video explains the basic transformations of graphs, including vertical and horizontal shifts, using simple examples.

Transcript

in this video we're going to look at some basic transformations of graphs so we'll start by letting C be a positive number and y be equal to f of X so the first few transformations we're going to look at involve vertical and horizontal shifts the first one is f of X plus C this means we shift up by C units so we shift the graph of f of f up C units... Read More

Key Insights

• 🚦 Vertical shifts involve adding or subtracting values to shift the graph up or down.
• 🗯️ Horizontal shifts involve adding or subtracting values to shift the graph left or right.
• 👉 Adding to the x variable shifts the graph left (horizontal), while subtracting shifts it right.
• 🚦 Adding to the function shifts the graph up (vertical), while subtracting shifts it down.
• 💯 Understanding the core function helps determine the direction of the shift.
• 📈 Examples shown include shifting a quadratic graph up, shifting a square root graph left, shifting an absolute value graph down, and shifting another quadratic graph left.
• 📈 The inverse relationship between adding and subtracting in graph transformations can be initially confusing but can be memorized easily.

Questions & Answers

Q: How do vertical shifts in graph transformations work?

Vertical shifts involve adding or subtracting values to the function, which shifts the graph up or down. Adding a positive value shifts the graph up, while subtracting a positive value shifts the graph down.

Q: How do horizontal shifts in graph transformations work?

Horizontal shifts involve adding or subtracting values to the x variable, which shifts the graph left or right. Adding a positive value to the x variable shifts the graph left, while subtracting a positive value shifts the graph right.

Q: What happens when you add a constant value to the core function in graph transformations?

When a constant value is added to the core function, the entire graph is shifted up by that value. For example, adding 3 to f(x) shifts the graph of f up by 3 units.

Q: What happens when you subtract a constant value from the core function in graph transformations?

When a constant value is subtracted from the core function, the entire graph is shifted down by that value. For example, subtracting 2 from f(x) shifts the graph of f down by 2 units.

Summary & Key Takeaways

• The video discusses vertical and horizontal shifts in graph transformations.

• Vertical shifts involve adding and subtracting values to shift the graph up or down.

• Horizontal shifts involve adding and subtracting values to shift the graph left or right.