Constants play a big part in how we understand different types of functions in Algebra I. Each function—like linear, quadratic, and exponential—feels different because of these constants.

Linear Functions

For linear functions, which look like this: (y = mx + b):

• (m) is the slope. It decides how steep the line is.
• (b) is the y-intercept. This tells us where the line crosses the y-axis.

Here's a fun fact: If you change (b), the whole line moves up or down but stays the same steepness!

Quadratic Functions

Now, let’s talk about quadratic functions, which look like this: (y = ax^2 + bx + c):

• (a) affects how wide or narrow the parabola is. If (a > 0), it goes up, and if (a < 0), it goes down.
• (b) and (c) help position the parabola on the graph.

If you adjust (c), you can move the entire parabola up or down!

Exponential Functions

Finally, we have exponential functions that look like this: (y = ab^x):

• (a) shows the starting value of the graph.
• (b) tells us if the function is growing (when (b > 1)) or decreasing (when (0 < b < 1)).

In all these functions, constants are really important. They help us understand how these equations work in real life!