Algebra Class: Functions and Their Properties

Which of the following equations best represents the quadratic function based on the provided values of x and f(x)?

Which function listed is an odd function?

What is the domain of the function $f(x) = \frac{3x - 1}{7}$?

What is the value of f(g(-1)) + g(f(1)) given the functions f(x) = x^2 and g(x) = 4 - 2x?

What are the domain and range of the function $f(x) = \sqrt{16 - x^2}$?

What is the result of the composition (f ∘ g)(x) if f(x) = x + 1 and g(x) = \frac{x - 1}{x + 1}?

What is the inverse of the function $f(x) = \frac{3x + 7}{7}$?

Which of the following functions does NOT contain a maximum value?

Quadratic Functions

A quadratic function is a polynomial function of degree two.
The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.
The graph of a quadratic function is a parabola.
The vertex of the parabola is the point where the function reaches its maximum or minimum value.

Odd and Even Functions

A function f(x) is an odd function if f(-x) = -f(x) for all x in the domain.
A function f(x) is an even function if f(-x) = f(x) for all x in the domain.

Domain and Range

The domain of a function is the set of all possible input values (x-values).
The range of a function is the set of all possible output values (y-values).

Function Composition

The composition of two functions f(x) and g(x) is denoted by (f∘g)(x) and is defined as f(g(x))
The composition of functions is a way of combining two functions to create a new function.

Inverse Functions

The inverse of a function f(x) is denoted by f^-1(x) and is defined as the function that "undoes" the effect of f(x).
The inverse of a function only exists if the function is one-to-one, which means that each input value has a unique output value.
To find the inverse of a function, switch the x and y variables and then solve for y.

This quiz covers essential concepts of functions including quadratic functions, odd and even functions, domain and range, function composition, and inverse functions. Test your understanding of these fundamental topics in algebra and enhance your mathematical skills.