5: Functions
- Page ID
- 45051
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By the end of this chapter, the student should be able to
- Evaluate and define a function
- Identify the independent and dependent variable and their units
- Apply algebraic operations on functions
- Recognize the shape of a function’s graph with its name and formula
There are many different types of equations that we can work with in algebra because an equation gives the relationship between a variable(s) and numbers. For example,
\[\dfrac{(x-3)^2}{9}-\dfrac{(y+2)^2}{4}=1\quad\text{or}\quad y=x^2-2x+7\quad\text{or}\quad\sqrt{y+x}-7=xy\nonumber\]
all give relationships between variables and numbers. Some of these relationships are called functions.
A function is when one input of a relation is linked to only one output of the relation, i.e., a function has only one \(y\) for one \(x\).
Function notation is represented by \(f(x)\) such that \[f(x) = y,\nonumber\] and we say \(f\) is a function of \(x\).
- 5.1: Introduction to functions
- A great way to visualize the definition of a function is to look at the graphs of a few relationships.
- 5.2: Linear Functions
- Previously, we discussed graphing linear equations. Putting it all together with functions, we now discuss linear functions. We treat linear functions in the same manner as linear equations, except for the condition that linear functions have only one output for every input.