Get ready to learn about horizontal shifts in functions! This is when we change how we see graphs by moving them. Understanding horizontal shifts is really important for getting good at transformations!

What Are Horizontal Shifts?

Horizontal shifts happen when we slide the graph of a function left or right along the x-axis. Exciting, right? This means that every point on the graph moves a certain number of spaces to create a new graph! The important formula to remember is:

$$y = f(x - h)$$

Here, $h$ stands for how much we shift the graph.

How Do They Work?

1. To the Right: If $h$ is a positive number, the graph shifts to the right! For example, if we take the function $f(x) = x^2$, then the new function $g(x) = f(x - 3) = (x - 3)^2$ shifts the whole graph 3 units to the right. How cool is that?

2. To the Left: If $h$ is a negative number, the graph shifts to the left! Using the same function, if we have $g(x) = f(x + 2) = (x + 2)^2$, the graph shifts left by 2 units. Wow, what a neat change!

Visualizing the Change

Let's think about a point on the graph, like (1,1). When we use a horizontal shift:

• If we shift right by 3 units, this point moves to (4,1).
• If we shift left by 2 units, it goes to (-1,1).

And this change happens for every point on the graph!

Why Does This Matter?

Horizontal shifts not only change where the graph is, but they also help us understand how functions work. They let us move graphs around to find where they meet, look for trends, and even solve real-life problems!

Key Takeaways

• Positive h: Shift right on the x-axis.
• Negative h: Shift left on the x-axis.
• The general formula for the shift is $y = f(x - h)$.

Next time you draw a function, think about how you can move it around with horizontal shifts! These changes make graphing more fun and interesting. Jump into graphing with these ideas, and watch how the world of functions changes right before your eyes! Happy learning!