Questions and Answers
What is the general form of a quadratic function?
What is the operation to combine two functions f(x) and g(x) to get (f + g)(x)?
What is the name of the function that maps each input to a unique output?
What is the point at which the graph of a function crosses the x-axis?
Signup and view all the answers
What is the type of function that is represented as f(x) = a^x?
Signup and view all the answers
What is the range of a function?
Signup and view all the answers
What is the operation to combine two functions f(x) and g(x) to get (f ∘ g)(x)?
Signup and view all the answers
What is the name of the function that is both injective and surjective?
Signup and view all the answers
What is the graph feature that a function approaches as x approaches a certain value?
Signup and view all the answers
What is the type of function that is represented as f(x) = p(x) / q(x)?
Signup and view all the answers
Study Notes
Functions in Algebra
Definition
- A function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range).
- In algebra, functions are often represented using variables and mathematical operations.
Types of Functions
- Linear Functions: of the form f(x) = mx + b, where m is the slope and b is the y-intercept.
- Quadratic Functions: of the form f(x) = ax^2 + bx + c, where a, b, and c are constants.
- Polynomial Functions: of the form f(x) = a_n x^n + a_(n-1) x^(n-1) + ... + a_1 x + a_0, where n is a non-negative integer.
- Rational Functions: of the form f(x) = p(x) / q(x), where p(x) and q(x) are polynomial functions.
- Exponential Functions: of the form f(x) = a^x, where a is a constant.
- Logarithmic Functions: of the form f(x) = log_a(x), where a is a constant.
Function Operations
- Function Addition: (f + g)(x) = f(x) + g(x)
- Function Subtraction: (f - g)(x) = f(x) - g(x)
- Function Multiplication: (f * g)(x) = f(x) * g(x)
- Function Composition: (f ∘ g)(x) = f(g(x))
Function Properties
- Domain: the set of input values for which the function is defined.
- Range: the set of output values of the function.
- Injective (One-to-One): a function that maps each input to a unique output.
- Surjective (Onto): a function that maps each output to at least one input.
- Bijective: a function that is both injective and surjective.
Graphing Functions
- X-Intercept: the point at which the graph crosses the x-axis.
- Y-Intercept: the point at which the graph crosses the y-axis.
- Asymptotes: lines that the graph approaches as x approaches a certain value.
- Maxima and Minima: the highest and lowest points of the graph.
Functions in Algebra
Definition
- A function is a relation between a set of inputs (domain) and a set of possible outputs (range).
- Functions are represented using variables and mathematical operations.
Types of Functions
- Linear Functions: f(x) = mx + b, where m is the slope and b is the y-intercept.
- Quadratic Functions: f(x) = ax^2 + bx + c, where a, b, and c are constants.
- Polynomial Functions: f(x) = a_n x^n + a_(n-1) x^(n-1) +...+ a_1 x + a_0, where n is a non-negative integer.
- Rational Functions: f(x) = p(x) / q(x), where p(x) and q(x) are polynomial functions.
- Exponential Functions: f(x) = a^x, where a is a constant.
- Logarithmic Functions: f(x) = log_a(x), where a is a constant.
Function Operations
- Function Addition: (f + g)(x) = f(x) + g(x).
- Function Subtraction: (f - g)(x) = f(x) - g(x).
- Function Multiplication: (f * g)(x) = f(x) * g(x).
- Function Composition: (f ∘ g)(x) = f(g(x)).
Function Properties
- Domain: the set of input values for which the function is defined.
- Range: the set of output values of the function.
- Injective (One-to-One): a function that maps each input to a unique output.
- Surjective (Onto): a function that maps each output to at least one input.
- Bijective: a function that is both injective and surjective.
Graphing Functions
- X-Intercept: the point at which the graph crosses the x-axis.
- Y-Intercept: the point at which the graph crosses the y-axis.
- Asymptotes: lines that the graph approaches as x approaches a certain value.
- Maxima and Minima: the highest and lowest points of the graph.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers the definition and types of functions in algebra, including linear, quadratic, and polynomial functions.
