Explore the fundamental concepts of functions in mathematics, including their definition as unique associations between sets, and their essential characteristics like domain and range. Functions are depicted through various graphical forms, such as lines for linear functions and parabolas for quadratic functions. The text delves into function evaluation, graphical interpretation, and advanced functions like exponential and logarithmic types.
Show More
Functions are mathematical rules that uniquely associate elements of one set with elements of another set
Symbols used in function notation
Function notation uses symbols like f(x) to represent the name and variable of a function
Evaluating functions
To evaluate a function, substitute a value for the variable and perform the prescribed operations
The domain is the set of allowable inputs, while the range is the set of all possible outputs for a function
Function diagrams visually show the relationship between inputs and outputs
Plotting points
To graph a function, plot points corresponding to input and output values and connect them to show the function's behavior
Types of functions and their graphs
Different types of functions, such as linear, quadratic, and trigonometric, have characteristic graphical forms
The vertical line test is a graphical technique used to determine if a curve represents a function
The domain of a function is the set of all input values for which the function is defined, while the range is the set of all output values it can produce
Basic types of functions
Linear, quadratic, and trigonometric functions are common types of functions with characteristic graphical forms
Complex functions
Functions can also be more complex, such as higher-degree polynomials, exponential, and logarithmic functions
00
A function is often symbolized as ______, where 'x' signifies the ______ and '______' denotes the resulting output.
f(x)
input variable
f(x)
01
Define 'domain' in functions.
Domain: Set of all allowable inputs for a function.
02
Define 'range' in functions.
Range: Set of all possible outputs from a function.
