Properties of Functions & Interval Notation

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is interval notation?

Back

Interval notation is a mathematical notation used to represent a range of values, typically expressed using parentheses and brackets to indicate whether endpoints are included.

Front

What does the notation (-∞, -2) U (5, ∞) represent?

Back

It represents the union of two intervals: all real numbers less than -2 and all real numbers greater than 5.

Front

What does the notation [-2, 5] represent?

Back

It represents the closed interval including all real numbers from -2 to 5, where -2 and 5 are included.

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints (e.g., (a, b)), while closed intervals do include their endpoints (e.g., [a, b]).

Front

How do you find the y-intercept of a linear function?

Back

The y-intercept is found by setting x = 0 in the function's equation and solving for y.

Front

How do you find the x-intercept of a linear function?

Back

The x-intercept is found by setting y = 0 in the function's equation and solving for x.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a function of the form y = ab^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.