Algebra Functions

Domain and Range

• Domain: The set of all possible input values (x-values) of a function
• Range: The set of all possible output values (y-values) of a function

Types of Functions

• Linear Function: A function of the form f(x) = mx + b, where m is the slope and b is the y-intercept
• Quadratic Function: A function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants
• Exponential Function: A function of the form f(x) = a^x, where a is a constant
• Polynomial Function: A function of the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_i are constants

Graphing Functions

• x-intercept: The point at which the graph crosses the x-axis
• y-intercept: The point at which the graph crosses the y-axis
• Asymptote: A line that the graph approaches as x approaches a certain value
• Maximum/Minimum: The highest/lowest point on the graph

Graph Characteristics

• Increasing/Decreasing: A function is increasing if its graph slopes upward, and decreasing if its graph slopes downward
• Concave Up/Down: A function is concave up if its graph opens upward, and concave down if its graph opens downward
• Inflection Point: A point at which the graph changes from concave up to concave down, or vice versa

Graphing Techniques

• Vertical Line Test: A function is a graph if every vertical line intersects the graph at most once
• Horizontal Line Test: A function is one-to-one if every horizontal line intersects the graph at most once
• Transformations: Functions can be transformed by shifting, stretching, and reflecting the graph

Domain and Range

• Domain is the set of all possible input values (x-values) of a function
• Range is the set of all possible output values (y-values) of a function

Types of Functions

• Linear Function: f(x) = mx + b, where m is the slope and b is the y-intercept
• Quadratic Function: f(x) = ax^2 + bx + c, where a, b, and c are constants
• Exponential Function: f(x) = a^x, where a is a constant
• Polynomial Function: f(x) = a_nx^n + a_(n-1)x^(n-1) +...+ a_1x + a_0, where a_i are constants

Graphing Functions

• x-intercept: the point at which the graph crosses the x-axis
• y-intercept: the point at which the graph crosses the y-axis
• Asymptote: a line that the graph approaches as x approaches a certain value
• Maximum/Minimum: the highest/lowest point on the graph

Graph Characteristics

• Increasing Function: graph slopes upward
• Decreasing Function: graph slopes downward
• Concave Up Function: graph opens upward
• Concave Down Function: graph opens downward
• Inflection Point: a point at which the graph changes from concave up to concave down, or vice versa

Graphing Techniques

• Vertical Line Test: a function is a graph if every vertical line intersects the graph at most once
• Horizontal Line Test: a function is one-to-one if every horizontal line intersects the graph at most once
• Transformations: functions can be transformed by shifting, stretching, and reflecting the graph

This quiz covers the basics of algebra functions, including domains and ranges, as well as types of functions such as linear, quadratic, and exponential functions.