## Podcast Beta

## Questions and Answers

What is the notation for a function?

What is the set of all possible output values of a function called?

What type of system of equations has a unique solution?

What is the method of solving systems of equations by substituting one equation into the other?

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What is the horizontal axis of a coordinate plane?

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What is the graph of a function that opens upward?

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What is the notation for an inequality that is greater than?

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What is the solution to the inequality 2x + 3 > 5?

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## Study Notes

### Functions

- A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range)
- Notation: f(x) = output value
- Domain: set of all input values (x) for which the function is defined
- Range: set of all possible output values (y)
- Key concepts:
- Function notation: f(x) = 2x + 1
- Domain and range: identify the domain and range of a function
- Evaluating functions: find the output value for a given input value
- Composition of functions: combine two or more functions
- Inverse functions: find the input value for a given output value

### Systems of Equations

- A system of equations is a set of two or more equations that must be true at the same time
- Types of systems:
- Independent systems: have a unique solution
- Dependent systems: have infinitely many solutions
- Inconsistent systems: have no solution

- Methods for solving systems:
- Substitution method: substitute one equation into the other
- Elimination method: add or subtract equations to eliminate one variable
- Graphing method: graph the equations on the same coordinate plane

### Graphing

- Graphing is a visual representation of a function or equation
- Key concepts:
- X-axis: horizontal axis, represents the input values (x)
- Y-axis: vertical axis, represents the output values (y)
- Origin: point where the x-axis and y-axis intersect (0, 0)
- Quadrants: four regions of the coordinate plane
- Graphing functions: identify the graph of a function
- Graphing equations: identify the graph of an equation
- Intercepts: find the x-intercepts and y-intercepts of a graph

### Inequalities

- An inequality is a statement that one expression is greater than, less than, or equal to another expression
- Notation: >, <, â‰¥, â‰¤, â‰
- Key concepts:
- Solving linear inequalities: solve for x
- Graphing linear inequalities: graph the solution on a number line
- Compound inequalities: solve and graph systems of inequalities

### Polynomials

- A polynomial is an expression consisting of variables and coefficients combined using only addition, subtraction, and multiplication
- Types of polynomials:
- Monomials: single term polynomials
- Binomials: two-term polynomials
- Trinomials: three-term polynomials

- Key concepts:
- Adding and subtracting polynomials: combine like terms
- Multiplying polynomials: use the distributive property
- Factoring polynomials: express a polynomial as a product of simpler polynomials
- Solving polynomial equations: solve for x

### Functions

- A function is a relation between a set of inputs (domain) and a set of possible outputs (range), where each input value corresponds to exactly one output value.
- Function notation is f(x) = output value, where x is the input value and f(x) is the output value.
- The domain is the set of all input values (x) for which the function is defined, while the range is the set of all possible output values (y).
- Evaluating functions involves finding the output value for a given input value, using the function notation.
- Composition of functions involves combining two or more functions, whereas inverse functions involve finding the input value for a given output value.

### Systems of Equations

- A system of equations is a set of two or more equations that must be true at the same time, and can be classified as independent (unique solution), dependent (infinitely many solutions), or inconsistent (no solution).
- The substitution method involves substituting one equation into the other, while the elimination method involves adding or subtracting equations to eliminate one variable.
- The graphing method involves graphing the equations on the same coordinate plane to find the solution.

### Graphing

- Graphing is a visual representation of a function or equation, where the x-axis represents the input values (x) and the y-axis represents the output values (y).
- The origin is the point where the x-axis and y-axis intersect, at (0, 0), and the quadrants are the four regions of the coordinate plane.
- Graphing functions and equations involves identifying the graph of a function or equation, while intercepts involve finding the x-intercepts and y-intercepts of a graph.

### Inequalities

- An inequality is a statement that one expression is greater than, less than, or equal to another expression, and can be notated as >, <, â‰¥, or â‰¤.

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## Description

Test your knowledge of functions, including function notation, domain, and range. Learn how to evaluate functions and compose functions.