Functions & Function Notation

Front

What is a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if no vertical line intersects the graph at more than one point.

Front

What is function notation?

Back

Function notation is a way to represent functions using symbols, typically written as f(x) to denote the output of the function f for the input x.

Front

What does f(x) = 2x - 3 represent?

Back

It represents a linear function where for every x-value, you can find a corresponding y-value by multiplying x by 2 and then subtracting 3.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function by checking if any vertical line crosses the curve more than once.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.

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 one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements; each output is unique to its input.

Front

How do you write a function in standard form?

Back

A function in standard form is typically written as Ax + By = C, where A, B, and C are constants.