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# Algebra 1: Function Notation Flashcards

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@ReliableDiction

### What is a function?

• An unordered pair of numbers
• A set of equations with no outputs
• A method to solve algebraic expressions
• A rule that establishes a relationship between two quantities (correct)
• ### What does the domain of a function represent?

All x values (input) and independent variable

### What does the range of a function represent?

All y values (output) and dependent variable

### What are the steps to solve functions through a mapping diagram?

<ol> <li>Label the input and output sections. 2) Ensure each input has exactly one output. 3) Write 'It's a function' or 'Not a function' and explain why.</li> </ol> Signup and view all the answers

### What is the slope in a function?

<p>Change in y/change in x</p> Signup and view all the answers

### What does the vertical line test determine?

<p>Whether a graph represents a function</p> Signup and view all the answers

### What is function notation?

<p>A way to name a function defined by an equation</p> Signup and view all the answers

### How do you solve a function notation as f(x) = #?

<p>Substitute the value into the equation and solve for x.</p> Signup and view all the answers

### How do you solve function notation as f(#)?

<p>Substitute the given x-value into the equation and solve for y.</p> Signup and view all the answers

### What is a piecewise function?

<p>A function made up from pieces of other functions</p> Signup and view all the answers

### What are the steps to solve piecewise functions?

<ol> <li>Find f(#) using the rules assigned to it. 2) Mark appropriate points on a number line or table. 3) Plot and determine if the function is continuous.</li> </ol> Signup and view all the answers

### What is a helpful tip when using a calculator for exponents?

<p>Surround the number and its sign with ( ) for accurate calculations.</p> Signup and view all the answers

## 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.

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## 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.

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