Algebra 1: Function Notation Flashcards

Study Notes

Function Fundamentals

A function is a rule connecting input (independent variable, x) to output (dependent variable, y) with exactly one output per input.

Domain and Range

The domain comprises all possible x values (inputs).
The range includes all possible y values (outputs).

Mapping Diagrams

Use a mapping diagram by labeling input and output sections.
Ensure each input has one output; repeated inputs are not allowed, but repeated outputs are permissible.
Determine if the relationship is a function with a concluding statement.

Solving Functions Using Tables

Calculate slope as change in y over change in x; check for a constant rate of change.
Locate points, preferably starting with ones having zeros or lower values for easier calculations.
Derive function rules using the equation y = mx + b, substituting a chosen point to find b.

Vertical Line Test (VLT)

To confirm a function graphically, draw vertical lines; if each line intersects the graph once, it qualifies as a function.

Function Notation

Function notation represents a function defined by an equation, e.g., f(x) = mx + b.
f(x) can substitute other letters, remaining equivalent to y.

Solving f(x) =

Substitute the given value for f(x) into the equation, then solve to find the x value.
Present the answer in function notation, e.g., f(3) = 10 signifies when x = 3, y is 10.

Solving f(#)

Identify the x value from the notation to find the corresponding y.
Input the x in the equation and solve, expressing the outcome in function notation.

Graphing Linear Functions

Find the domain (x values) and range (y values) for the graph.
Solve for specific f(x) and f(#) as per the problem's demand, utilizing the graph for accuracy.

Piecewise Functions

Piecewise functions consist of segments from various functions, governed by inequalities.

Solving Piecewise Functions

Apply the defined rules to evaluate f(#) using inequalities; create a table to categorize points.
Distinguish between open and closed circles based on the inequalities.
Analyze continuity based on the line's connectivity and ability to be traced without lifting the pencil.

Calculator Tips

For exponents, enclose the number and its sign in parentheses when inputting into a calculator to ensure accuracy.

Description

These flashcards cover essential terms related to function notation in Algebra 1, including definitions of function, domain, and range. Perfect for mastering the concepts of input and output relationships, this resource helps reinforce understanding through key terms and concepts integral to graphing and solving functions.