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Questions and Answers
What is the set of all possible input values of a function?
What is the set of all possible input values of a function?
What is the form of a quadratic function?
What is the form of a quadratic function?
What is the point at which the graph crosses the x-axis?
What is the point at which the graph crosses the x-axis?
What is the term for a function that is increasing if its graph slopes upward?
What is the term for a function that is increasing if its graph slopes upward?
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What is the term for a function that opens upward?
What is the term for a function that opens upward?
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What is the test used to determine if a graph is a function?
What is the test used to determine if a graph is a function?
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What is the process of shifting, stretching, and reflecting the graph?
What is the process of shifting, stretching, and reflecting the graph?
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What is the term for a point at which the graph changes from concave up to concave down, or vice versa?
What is the term for a point at which the graph changes from concave up to concave down, or vice versa?
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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
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Description
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.