Florida End Of Course Assessment: Algebra

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Unit 1: Functions, Linear Equations, and Inequalities

There's a lot to be said about functions and even more to be said about dysfunctions. How does that saying go? "We put the fun in dysfunctional"? Or was it "We put the ram in the rama lama ding dong"? We'll save that question for another day.

About 55% of the Algebra I EOC exam is all about functions, so you can't function without them. Okay, you could, but you probably wouldn't do so well on the test. Don't worry; we'll do our best to make functions as fun(ctional) as possible.

First, though, we'll stop with the puns about functions. Or would that be the punctions?

To ensure your victory on exam day, you'll need to know what functions are, how to describe and determine them, and how to treat them. (We suggest following the Golden Rule for that last bit.) You'll also need to know how to solve and graph lines, inequalities, and systems of linear equations or inequalities.


The Big Issues

In this section, we'll focus on understanding and interpreting functions as well as solving linear equations and inequalities. There will be other topics sprinkled throughout, but getting these two big issues down will put you on the road to success.

Understanding and Interpreting Functions

We'll start by describing a functional relationship with words. In fact, that's one of the official ways to represent a function...and usually the way we first encounter a functional relationship.

There's a joke in here somewhere, we just know it.

However, words are only one way to understand functions. We can graph the relationship using the coordinate plane. We can whip up a table to show some examples of data points, also known as coordinate pairs. And, if we're feeling really sassy, we can even create an equation chock full of numbers and variables.

These are all different ways to understand functions, so you'll need to be comfortable when it comes to using and moving among the various representations of functions. Basically, functions are specific mathematical relationships in which we have one output for every input. In this section, get to know this idea input and out—er, inside and out—and apply it to coordinate pairs, graphs, and equations.

Solving Linear Equations and Inequalities

Solving linear equations and inequalities can be as simple as choosing the right point on a coordinate plane or as cumbersome as changing the inequality sign more often than you change your underwear.

We hope that's cumbersome, anyway. If not, you may want to reconsider your laundry schedule.

Solving a linear equation or inequality basically means finding a value or set of values that satisfies the relationship. Usually, there will be a graph, equation, or enough information to come up with one on our own. There will not be blood. We can use any of the above to find whatever values we want; most questions will typically ask us to find the value of x, the value of y, or both.

For instance, if we have a (Facebook-official) relationship between x and y where x = y, one solution would be when x = 2 and y = 2. If we're given y = 3, however, the x-value can no longer equal 2; x needs to be 3. If we had x < y, on the other hand, x = 2 could still stick around when y = 3 because the two values satisfy the inequality.

Matters become a little more (Facebook) complicated when we're dealing with a system of equations or inequalities, which means that there are more than one of them. The most common questions about systems will ask you to find the x- and y-values that satisfy both equations or inequalities.

What can we say? They're people pleasers.

Finally, know that solving a system of equations graphically means finding the intersection point. The coordinate will give us our x- and y-value; it's the same deal with inequalities, only our dreams come true and we're finally allowed to shade in parts of the graph. Make sure to choose pretty colors and stay inside the lines.