Algebra 1: Function Notation Flashcards

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.