8 Questions
What is the set of all possible input values of a function?
Domain
What is the form of a quadratic function?
f(x) = ax^2 + bx + c
What is the point at which the graph crosses the x-axis?
x-intercept
What is the term for a function that is increasing if its graph slopes upward?
Increasing
What is the term for a function that opens upward?
Concave Up
What is the test used to determine if a graph is a function?
Vertical Line Test
What is the process of shifting, stretching, and reflecting the graph?
Transformations
What is the term for a point at which the graph changes from concave up to concave down, or vice versa?
Inflection Point
Study Notes
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.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
