Algebra Functions and Sequences Quiz

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Questions and Answers

What is an Arithmetic Sequence?

A sequence that does not follow a rule

A sequence of numbers in which the difference between any two consecutive terms is the same (correct)

A sequence where terms are multiplied by a constant

A sequence of prime numbers

What does Average Rate of Change refer to?

The change in the value of a quantity by the elapsed time

What is a Coefficient?

A number multiplied by a variable in an algebraic expression

Define Constant Rate of Change.

The slope of a linear function's graph Signup and view all the answers

What does the term Continuous refer to in mathematics?

A connected set of numbers such as an interval Signup and view all the answers

What is the meaning of Discrete?

A set with elements that are disconnected Signup and view all the answers

What is Domain in a function?

The set of x-coordinates of the set of points on a graph Signup and view all the answers

What are End Behaviors of a graph?

The appearance of a graph as it is followed farther in either direction Signup and view all the answers

Define Explicit Expression.

A formula that allows direct computation of any term for a sequence Signup and view all the answers

What is an Exponential Function?

A nonlinear function where the independent value is an exponent Signup and view all the answers

What is the purpose of an Exponential Model?

To represent real-world phenomena using an exponential function Signup and view all the answers

What is an Expression in mathematics?

Any mathematical calculation or formula combining numbers and/or variables Signup and view all the answers

An Even Function is symmetric with respect to the y-axis.

True Signup and view all the answers

What is a Factor?

Numbers that can be evenly divided into a given number Signup and view all the answers

Define Geometric Sequence.

A sequence where the ratio between consecutive terms is the same Signup and view all the answers

What does Horizontal Shift mean?

A rigid transformation of a graph in a horizontal direction Signup and view all the answers

What is Interval Notation?

A notation representing an interval as a pair of numbers Signup and view all the answers

Define Linear Function.

A function with a constant rate of change and a straight line graph Signup and view all the answers

What is a Linear Model?

A linear function representing real-world phenomena Signup and view all the answers

An Odd Function is symmetric with respect to the origin.

True Signup and view all the answers

What is a Parameter?

The independent variable or variables in a system of equations with multiple dependent variables Signup and view all the answers

What is a Quadratic Equation?

An equation of degree 2, which has at most two solutions Signup and view all the answers

Define Quadratic Function.

A function of degree 2 resembling a parabola Signup and view all the answers

What is a Root in a function?

The x-values where the function has a value of zero Signup and view all the answers

What does Range refer to in a function?

The set of all possible outputs of a function Signup and view all the answers

What is a Recursive Formula?

A formula that requires computation of all previous terms to find a term value Signup and view all the answers

Define Slope.

The ratio of the vertical and horizontal changes between two points Signup and view all the answers

What is a Term in a sequence?

A value in the sequence; the first term is the 1st term, second is the 2nd term, and so on Signup and view all the answers

What does Vertical Translation mean?

A shift in which a figure moves vertically Signup and view all the answers

Define X-intercept.

The point where a line meets or crosses the x-axis Signup and view all the answers

What does Y-intercept refer to?

The point where a line meets or crosses the y-axis Signup and view all the answers

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.