Recent Lessons

Show all results for ""

Feature Overview

Ace your exams with our all-in-one platform for creating and sharing quizzes and tests.

Quizzes

Create quizzes and tests automatically from your content using AI.

Flashcards

Automatically turn your notes into digital flashcards.

Share, Export & Embed

Share with classmates or export to Excel and your learning management system.

Stats & Reporting

Auto-grading quizzes and tests with detailed stats and reports.

Mobile Apps

The smarter way to study – wherever you are.

Pricing

Search...

15 Questions

100 Views

Algebra 2 Unit 7 Lesson 9 Flashcards

Choose a study mode

Play Quiz

Study Flashcards

Spaced Repetition

Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

When we compose functions, we must make sure that the output of the first function is part of the ___ of the second function.

Domain (correct)

Range

Preimage

Image

In general, the composition of functions is not ___.

Linear

Distributive

Associative

Commutative (correct)

We expect to see a ___ for the graph of a composition of a function and its inverse function, if the domain of each is all real numbers.

Line (correct)

Curve

Circle

Parabola

Find the composition of the function.

x'^{1/6} Signup and view all the answers

Find the composition of the function.

x'^{1/6} Signup and view all the answers

Find the composition of the function.

x'^{-1/2} Signup and view all the answers

Find the composition of the function.

x'^{-1/2} Signup and view all the answers

Find the composition of the function.

x'^{6} Signup and view all the answers

Find the composition of the function.

x'^{6} Signup and view all the answers

Find the composition of the function.

1/x + 5 Signup and view all the answers

Find the composition of the function.

1/x + 5 Signup and view all the answers

Find the composition of the function.

x - 3 Signup and view all the answers

Find the composition of the function.

x - 6 \sqrt{x} = 9 Signup and view all the answers

Find the equation of the circle with center (-2, 5) and radius 5.

(x + 2)^2 + (y - 5)^2 = 25 Signup and view all the answers

Find the product (x + 3)^3.

x^3 + 9x^2 + 27x + 27 Signup and view all the answers

Study Notes

Function Composition

Ensure the output of the first function is included in the domain of the second function for proper composition.
The composition of functions is generally not commutative, meaning the order of functions matters.

Graphs and Inverses

A graph representing the composition of a function and its inverse, when both have domains as all real numbers, should ideally form a line.

Composition Examples

Compositions can yield outputs such as:
- x^(1/6) for certain functions.
- x^(-1/2) reflecting exponentiation rules.
- x^6 illustrating polynomial growth.

Rational Functions

Compositions may produce forms like 1/(x+5), demonstrating how functions interact through division.

Linear Functions

Finding compositions can lead to linear transformations, such as results of x-3 or adjusting constants in expressions like x-6.

Circle Equation

The equation for a circle centered at (-2, 5) with a radius of 5 follows the standard form:
- (x+2)² + (y-5)² = 25.

Polynomial Expansion

Expanding functions results in expressions such as the product of (x+3)³, yielding:
- x³ + 9x² + 27x + 27, showcasing the binomial expansion.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your understanding of function composition with this set of flashcards designed for Algebra 2, Unit 7, Lesson 9. Each card presents a question about key concepts that are crucial for understanding function operations. Perfect for study and review before exams!