When learning about linear functions in Algebra II, it's important to understand some basic features.

A linear function is a special type of function that looks like a straight line when you draw it on a graph. The main way to write a linear function is:

$$f(x) = mx + b$$

In this equation, $m$ represents the slope, and $b$ tells you where the line crosses the y-axis.

Key Features of Linear Functions:

1. Slope ($m$):

   • The slope tells us how steep the line is.
   • If the slope is positive, the line goes up from left to right.
   • If the slope is negative, the line goes down from left to right.
   • For example, if $m = 2$, that means for every 1 unit you move to the right ($x$), the line goes up 2 units ($y$).

2. Y-Intercept ($b$):

   • The y-intercept is the point where the line crosses the y-axis.
   • This happens when $x$ is 0.
   • For instance, if $b = 3$, the line crosses the y-axis at the point (0, 3).

3. Domain and Range:

   • The domain of a linear function includes all real numbers, which means you can use any number for $x$.
   • The range is also all real numbers, because the straight line goes on forever in both directions.

4. Graph:

   • When you graph a linear function, it will always make a straight line.
   • This straight line shows that the function changes at a constant rate.
   • For example, the function $f(x) = 2x + 3$ has a slope of 2 and crosses the y-axis at the point (0, 3).

By knowing these features, you’ll be better at spotting and working with linear functions!