Transformations of Functions Flashcards

Questions and Answers

What is a parent function?

The most basic function in a family of functions.

What is the linear parent function?

y = x or f(x) = x. The simplest form of a linear equation.

What is the quadratic parent function?

y = x^2 or f(x) = x^2.

What is the exponential parent function?

y = ab^x. Signup and view all the answers

What does it mean to transform parent functions?

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

What are translations of parent functions?

Adding k or h to the x or y values to shift a graph left/right or up/down. Signup and view all the answers

What is reflection of parent functions?

Multiplying the x or y values to reflect over the y-axis or x-axis. Signup and view all the answers

What does rotation of parent functions involve?

Rearranging x and y values, sometimes multiplying by a negative, to rotate 90 degrees, 180 degrees, 270 and 360 degrees clock- and counter-clockwise. Signup and view all the answers

What is slope-intercept form?

y = mx + b. Signup and view all the answers

What is function notation?

An equation in the form of 'f(x)=' to show the output value of a function, f, for an input value x. Signup and view all the answers

What is the domain of a function?

The x values of a function. Signup and view all the answers

What is the range of a function?

The y values of a function. Signup and view all the answers

What are integer operations?

Operations with signed numbers that explain how to add, subtract, multiply, and divide positive and negative numbers. Signup and view all the answers

What is the distributive property?

a(b + c) = ab + ac. Signup and view all the answers

Study Notes

Parent Functions

Most basic function within a family of functions that serves as a reference point for transformations.

Linear Parent Function

Represented by the equation y = x or f(x) = x.
Known as the simplest form of a linear equation.

Quadratic Parent Function

Defined by the equation y = x² or f(x) = x².
Characteristic U-shaped graph.

Exponential Parent Function

Expressed in the form y = ab^x.
Models exponential growth or decay.

Transformations of Parent Functions

Modifications of parent functions create different members within the same family of graphs.

Translations of Parent Functions

Involves adding constants k or h to shift the graph horizontally (left/right) or vertically (up/down).

Reflection of Parent Functions

Involves multiplying x or y values to reflect the graph over the y-axis or x-axis.

Rotation of Parent Functions

Involves rearranging x and y values, potentially multiplying by a negative factor, to rotate graphs by angles of 90, 180, 270, and 360 degrees, in both clockwise and counter-clockwise directions.

Slope-Intercept Form

Written as y = mx + b, where m is the slope and b is the y-intercept.

Function Notation

Represented as f(x) = ?, indicating the output value of a function f for a specific input x.

Domain

Refers to the set of all possible x values for which a function is defined.

Range

Refers to the set of all possible y values that a function can output.

Integer Operations

Focus on operations involving signed numbers, detailing rules for adding, subtracting, multiplying, and dividing positive and negative integers.

Distributive Property

Defined by the equation a(b + c) = ab + ac, illustrating how multiplication distributes over addition.

Description

Explore the essential concepts of parent functions and their transformations with these flashcards. Each card defines key terms and equations relevant to various types of functions, including linear, quadratic, and exponential. Perfect for visual learners and students preparing for exams.