Page 184 - ABCTE Study Guide_Neat

• To solve problems about scale models and drawings, set up a proportion that you can
solve. Keep corresponding information together when you set up the proportion.
• Similar triangles provide another opportunity to use proportions to solve for the length of
the missing side.

All About Functions

Lesson Objective

In the following sections, we'll review variables and discuss functions. A function rule is an equation that
describes a function; we'll get some practice with this concept and then move on to linear functions.

Previously Covered

• We covered how ratios work and looked at some ways that you could apply them.
• We also reviewed proportions and saw how to use cross multiplication to compare
triangles, scale modes, and maps.

What's a Function?

Before getting into functions, there are a few other things we need to make sure that you understand first.

We'll begin with the concept of independent and dependent variables.

In the graph above, the independent variable is the number of hours worked. The change in the number
of hours affects the amount paid. The independent variable is almost always on the x-axis and is
represented by xin equations.

The dependent variable is the amount paid. The amount paid depends on the hours worked. The
dependent variable is almost always on the y-axis and is represented by y in equations.

The information in the graph can be represented in a table, showing the values of x and y. The information
can also be shown as ordered pairs (x, y).

A relation is any set of ordered pairs.
A function is a special kind of relation. Functions assign exactly one value of the dependent variable to
each value of the independent variable. Let's assume that x is the independent variable and y is the
dependent variable. To put it concisely:

In a function, there can only be one x-value for each y-value. There can be duplicate y-values but not
duplicate x-values in a function.