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Questions and Answers
What is an Arithmetic Sequence?
What is an Arithmetic Sequence?
What does Average Rate of Change refer to?
What does Average Rate of Change refer to?
The change in the value of a quantity by the elapsed time
What is a Coefficient?
What is a Coefficient?
A number multiplied by a variable in an algebraic expression
Define Constant Rate of Change.
Define Constant Rate of Change.
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What does the term Continuous refer to in mathematics?
What does the term Continuous refer to in mathematics?
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What is the meaning of Discrete?
What is the meaning of Discrete?
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What is Domain in a function?
What is Domain in a function?
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What are End Behaviors of a graph?
What are End Behaviors of a graph?
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Define Explicit Expression.
Define Explicit Expression.
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What is an Exponential Function?
What is an Exponential Function?
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What is the purpose of an Exponential Model?
What is the purpose of an Exponential Model?
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What is an Expression in mathematics?
What is an Expression in mathematics?
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An Even Function is symmetric with respect to the y-axis.
An Even Function is symmetric with respect to the y-axis.
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What is a Factor?
What is a Factor?
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Define Geometric Sequence.
Define Geometric Sequence.
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What does Horizontal Shift mean?
What does Horizontal Shift mean?
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What is Interval Notation?
What is Interval Notation?
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Define Linear Function.
Define Linear Function.
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What is a Linear Model?
What is a Linear Model?
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An Odd Function is symmetric with respect to the origin.
An Odd Function is symmetric with respect to the origin.
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What is a Parameter?
What is a Parameter?
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What is a Quadratic Equation?
What is a Quadratic Equation?
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Define Quadratic Function.
Define Quadratic Function.
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What is a Root in a function?
What is a Root in a function?
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What does Range refer to in a function?
What does Range refer to in a function?
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What is a Recursive Formula?
What is a Recursive Formula?
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Define Slope.
Define Slope.
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What is a Term in a sequence?
What is a Term in a sequence?
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What does Vertical Translation mean?
What does Vertical Translation mean?
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Define X-intercept.
Define X-intercept.
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What does Y-intercept refer to?
What does Y-intercept refer to?
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Study Notes
Arithmetic and Sequences
- An Arithmetic Sequence has a constant difference between consecutive terms.
- A Geometric Sequence features a consistent ratio between consecutive terms, known as the common ratio.
Functions and Their Properties
- The Average Rate of Change measures how a quantity changes relative to time, calculated as the change in y-values over the change in x-values between two points.
- A Linear Function has a constant rate of change and is represented graphically as a straight line.
- An Exponential Function has an independent variable as an exponent, taking the form y = ab^x.
Graphical Analysis
- End Behaviors describe graph behavior as it extends infinitely in either direction.
- X-intercept is where a line crosses the x-axis, while the Y-intercept is where it crosses the y-axis.
- Even Functions are symmetric with respect to the y-axis; Odd Functions are symmetric with respect to the origin.
Mathematical Concepts
- A Coefficient is a number that multiplies a variable in an expression.
- A Root refers to the x-values where a function equals zero.
- Constant Rate of Change represents the slope in a linear function graph.
Sequences and Formulas
- An Explicit Expression provides a direct way to calculate any term in a sequence.
- A Recursive Formula defines terms in relation to previous terms.
- Terms in a sequence are individual values, with position determining their order (e.g., first term, second term).
Evaluating Functions
- Domain encompasses all possible x-coordinates for a graph or function.
- Range represents all potential output values of a function.
Transformations
- A Horizontal Shift adjusts a graph left or right.
- A Vertical Translation shifts a figure up or down.
Equations and Models
- A Quadratic Equation is of degree 2 and can have up to two solutions.
- A Quadratic Function, also degree 2, has a parabolic graph that can open upwards or downwards.
- Linear Models and Exponential Models represent real-world data using linear and exponential functions, respectively.
Additional Concepts
- Factor refers to numbers that divide another number evenly.
- Parameter is an independent variable in a system of equations with multiple dependent variables.
- Interval Notation is used to express intervals with specific endpoints, indicated by parentheses (exclusive) or brackets (inclusive).
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Description
Test your knowledge of arithmetic and geometric sequences, along with various types of functions and their properties. This quiz covers concepts such as rate of change, intercepts, and function behaviors. Perfect for reinforcing your understanding of algebraic principles.