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