Functions as Equations flashcard

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the given value into the function's equation for the variable.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if no two ordered pairs have the same first element (input) with different second elements (outputs).

Front

What is function notation?

Back

Function notation is a way to write functions that clearly indicates the input variable. For example, f(x) = 2x - 3.

Front

How do you find f(1) if f(x) = 2x + 1?

Back

Plug a 1 in for all the x's: f(1) = 2(1) + 1 = 3.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, typically written as (x, y).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.

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.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be linear?

Back

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