Functions in Algebra Flashcards

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Questions and Answers

What is a function in algebra?

A function is a relation for which each value from the set of first components is associated with exactly one value from the set of second components of the ordered pair.

What is a function and not a function?

A function is a relation in which each input has only one output.

What are the 3 types of functions?

Linear, Quadratic, Exponential.

How many types of functions are there in math?

8 types. Signup and view all the answers

How do you write a function?

You write functions with a function name followed by the dependent variable, such as f(x), g(x), or h(t). Signup and view all the answers

How do you describe a function?

A function is a relation between a set of inputs and a set of permissible outputs, where each input is related to exactly one output. Signup and view all the answers

How do you know a function is a function?

By using the vertical line test on a graph. Signup and view all the answers

What is the definition of not a function?

Not functional; having no function or serving no useful purpose. Signup and view all the answers

Is an equation a function?

True Signup and view all the answers

What is a function in math easy definition?

A special relationship where each input has a single output, often written as 'f(x)'. Signup and view all the answers

What are the concepts of functions?

A function ties to a specific rule, formula, or computation defining an input-output process. Signup and view all the answers

What are the 7 parent functions?

Linear, Quadratic, Cubic, Absolute, Reciprocal, Exponential, Logarithmic. Signup and view all the answers

What are the two main types of functions?

Injective function and Surjective function. Signup and view all the answers

What are functions and its types?

A function maps each element of set A to one element of set B. Signup and view all the answers

What are the 5 functions in Excel?

VLookup Formula, Concatenate Formula, Text to Columns, Remove Duplicates, Pivot Tables. Signup and view all the answers

What are the 6 functions?

Sine, Cosine, Tangent, Cotangent, Secant, and Cosecant. Signup and view all the answers

What are the family functions in math?

A set of functions whose equations have a similar form, with the simplest form as the 'parent'. Signup and view all the answers

What is function how many types of function?

Many types of polynomial functions exist, typically categorized by their degree. Signup and view all the answers

Study Notes

Functions in Algebra

A function is defined as a relation where each input has exactly one corresponding output.
In a function, "y" is a function of "x," meaning each "x" value can only yield one "y" value, preventing multiple outputs for a single input.

Types of Functions

Three primary types of functions include:
- Linear
- Quadratic
- Exponential
Additional types of functions:
- One-to-one (Injective)
- Many-to-one
- Onto (Surjective)
- Into
- Polynomial
- Identical
- Linear
- Quadratic

Writing and Describing Functions

Functions can be written using a function name, like f(x), g(x), or h(t) for functions dependent on time.
Each function establishes a relationship between inputs and permissible outputs, exemplified by mapping a number to its square (e.g., f(x) = x^2).

Identifying Functions

The vertical line test is used to determine if a relation is a function; it must intersect the graph only once at any location.
An equation is a function if it fits the definition of associating each input with only one output; some equations do not satisfy this condition.

Parent and Family Functions

Parent functions are the simplest forms in a function family, examples include:
- Linear
- Quadratic
- Cubic
- Absolute
- Reciprocal
- Exponential
- Logarithmic
- Square Root
- Trigonometric functions (sine, cosine, tangent, cotangent, secant, cosecant)

Concepts and Characteristics

Functions are tied to specific rules or formulas, mapping input values to output values.
A function defines a unique output for each input value from two non-empty sets (A and B).

Functions in Excel

Key Excel functions include:
- VLookup
- Concatenate
- Text to Columns
- Remove Duplicates
- Pivot Tables

Summary of Function Types

Functions can be divided into different types, including polynomial functions based on their degree; a polynomial is a constant function if its degree is zero.

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Description

Test your understanding of functions in algebra with these flashcards. Learn the definitions and key concepts about relations, inputs, and outputs. Perfect for students looking to reinforce their knowledge in this fundamental area of mathematics.