Algebra Parent Functions Flashcards

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Questions and Answers

What is the linear function parent?

f(x)=x (correct)

f(x)=2^x

f(x)=x^2

f(x)=√x

What is the linear graphing form?

y-y1=m(x-x1)

What is the quadratic parent function?

f(x)=∛x

f(x)=2^x

f(x)=x^2 (correct)

f(x)=x^3

What is the quadratic graphing form?

y=a(x-h)^2+k Signup and view all the answers

What is the absolute value function parent?

f(x)= |x| Signup and view all the answers

What is the absolute value graphing form?

y=a|x-h|+k Signup and view all the answers

What is the square root function parent?

f(x)=√x Signup and view all the answers

What is the square root graphing form?

y=a√(x-h)+k Signup and view all the answers

What is the cubic function parent?

f(x)=x^3 Signup and view all the answers

What is the cubic function graphing form?

y=a(x-h)^3+k Signup and view all the answers

What is the cube root function parent?

f(x)=∛x Signup and view all the answers

What is the cube root graphing form?

y=a∛(x-h)+k Signup and view all the answers

What is the exponential function parent?

f(x)=2^x Signup and view all the answers

What is the reciprocal parent function?

f(x)= 1/x Signup and view all the answers

What is a function?

A relation between a set of inputs and outputs where each input has exactly one output. Signup and view all the answers

What does 'a' tell you in an equation?

The vertical stretch or compression factor and if the graph has been reflected over the x-axis. Signup and view all the answers

What does 'h' tell you in an equation?

The horizontal shift right or left. Signup and view all the answers

What does 'k' tell you in an equation?

The vertical shift up or down. Signup and view all the answers

What are transformations in graphing?

Changes made to a graph that doesn't alter the type of graph Signup and view all the answers

What is absolute value?

Distance of a point from zero. Signup and view all the answers

What does 'range' mean in mathematics?

All possible y values for a function. Signup and view all the answers

What does 'domain' mean in mathematics?

All possible x values for a function. Signup and view all the answers

Study Notes

Parent Functions Overview

Linear Function Parent: Defined by the equation f(x) = x, representing a straight line through the origin.
Quadratic Function Parent: Characterized by f(x) = x², resulting in a parabolic curve that opens upwards.
Absolute Value Function Parent: Expressed as f(x) = |x|, displaying a "V" shape graph, indicating distance from zero.
Square Root Function Parent: Given by f(x) = √x, featuring a graph that starts at the origin and increases gradually.
Cubic Function Parent: Defined by f(x) = x³, producing an S-shaped curve crossing through the origin.
Cube Root Function Parent: Given by f(x) = ∛x, which produces a curve allowing all real numbers.
Exponential Function Parent: Represented by f(x) = 2^x, revealing rapid growth for positive x values.
Reciprocal Function Parent: Defined by f(x) = 1/x, featuring two hyperbolas in opposite quadrants.

Graphing Forms

Linear Graphing Form: y - y₁ = m(x - x₁), representing a line on a graph using a point and a slope.
Quadratic Graphing Form: y = a(x - h)² + k, providing transformations through vertex form with 'a', 'h', and 'k'.
Absolute Value Graphing Form: y = a|x - h| + k, indicating transformations of the absolute value function.
Square Root Graphing Form: y = a√(x - h) + k, involving vertical/horizontal stretches and shifts of the square root function.
Cubic Graphing Form: y = a(x - h)³ + k, translating cubic functions while adjusting its steepness.
Cube Root Graphing Form: y = a∛(x - h) + k, similar transformations applicable as in other parent functions.

Function Characteristics

Function Definition: A relation connecting inputs to unique outputs, ensuring each input corresponds to only one output.
One-to-One Function: Each input maps to a unique output, and vice versa, ensuring no value is repeated in either domain or range.
Domain: Represents all possible x values that can be plugged into a function without resulting in undefined outputs.
Range: Encompasses all potential y values produced by the function as outputs across the domain.

Transformations and Features

Transformations: Graph alterations such as stretching, compressing, or reflecting, that retain the type of graph.
Absolute Value: Defines the numerical distance of any value from zero on the number line.
Parameter 'a': Indicates vertical stretch/shrink of the graph and shows reflection across the x-axis if negative.
Parameter 'h': Represents horizontal shifts, determining how far right (positive) or left (negative) the graph moves.
Parameter 'k': Determines vertical shifts, indicating movement up (positive) or down (negative) from the original graph position.

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Description

Test your knowledge of algebra parent functions with these flashcards. Each card presents a key concept, including definitions and graphing forms of linear, quadratic, and absolute value functions. Perfect for students looking to reinforce their understanding of these essential algebraic concepts.