Algebra 2 Functions Flashcards

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Questions and Answers

What is a function?

A relation with multiple outputs for one input

A collection of numbers

A relation where every input corresponds to exactly one output (correct)

A set of outputs in a relation

What is the domain in a relation?

The set of input values in a relation.

What is the range in a relation?

The set of output values in a relation.

What is a parent function?

The simplest function in a family of functions. Signup and view all the answers

What is a linear function?

A function that creates a straight line when graphed. Signup and view all the answers

What is a quadratic function?

A function that forms a parabola when graphed. Signup and view all the answers

What is an absolute value function?

A function that outputs the absolute value of its input. Signup and view all the answers

What is a square root function?

A function that outputs the square root of its input. Signup and view all the answers

What is a cubic function?

A function that creates a curve with one or two bends. Signup and view all the answers

What is a cube root function?

A function that outputs the cube root of its input. Signup and view all the answers

What is a rational function?

A function that can be expressed as the ratio of two polynomials. Signup and view all the answers

What is an exponential function?

A function in which an independent variable is in the exponent. Signup and view all the answers

What is a logarithmic function?

A function that is the inverse of an exponential function. Signup and view all the answers

What are transformations of parent functions?

Parent functions can be transformed to create other members in a family of graphs. Signup and view all the answers

What is a translation in terms of functions?

A shift of a parent function. Signup and view all the answers

What is a reflection in terms of functions?

A flip of the parent function. Signup and view all the answers

What is a dilation in terms of functions?

A stretch or compression of the parent function. Signup and view all the answers

What is the inverse of a function?

The graph of an inverse function is the reflection of the original graph over the line, y = x. Signup and view all the answers

What is point discontinuity?

A point at which a function is not defined. Signup and view all the answers

What is an asymptote?

A line that the graph of a function approaches but never reaches. Signup and view all the answers

Study Notes

Functions Overview

A function is a relation with unique outputs for each input; it pairs every domain element with a single range element.

Key Components of Functions

Domain refers to the set of all possible input values of a function.
Range consists of all possible output values that result from the function.

Types of Functions

Parent Function: The simplest function in a family that serves as a reference for other functions.
Linear Function: Characterized by a straight line, defined by the equation ( y = mx + b ), where ( m ) is the slope.
Quadratic Function: A polynomial function of degree 2, typically represented as ( y = ax^2 + bx + c ).
Absolute Value Function: Described by ( y = |x| ); contains all non-negative outputs for real numbers.
Square Root Function: Given by ( y = \sqrt{x} ), outputs non-negative values for non-negative inputs.
Cubic Function: A polynomial of degree 3, expressed as ( y = ax^3 + bx^2 + cx + d ).
Cube Root Function: Defined by ( y = \sqrt[3]{x} ), allowing both negative and positive outputs.
Rational Function: Expressed as the ratio of two polynomials, can have points of discontinuity.
Exponential Function: Written as ( y = a(b^x) ); typically shows rapid growth or decay.
Logarithmic Function: The inverse of the exponential function, generally noted as ( y = \log_b(x) ).

Transformations of Parent Functions

Transformations modify parent functions to derive other functions in the same family.
Translation: Involves shifting a parent function vertically or horizontally.
Reflection: A flip over the line ( y = x ); alters the orientation of the graph.
Dilation: Creates a stretch or compression, changing the rate of growth or decline of the function.

Special Features in Function Behavior

Inverse of a Function: The reflective counterpart across the line ( y = x ). Found by swapping ( x ) and ( y ) in the original equation.
Point Discontinuity: Represents locations where the function is not defined, leading to gaps in the curve.
Asymptote: A line that a function’s graph approaches closely but never intersects, indicating limits in function behavior.

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Description

Test your understanding of functions with these flashcards! This quiz covers essential concepts such as function definitions, domain, range, and parent functions. Enhance your algebra skills and prepare for advanced topics in mathematics.