Review of functions

Front

What is a function in mathematical terms?

Back

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

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is paired with more than one y-value.

Front

What does the term 'rate of change' refer to in the context of functions?

Back

The rate of change refers to how much the output value (y) changes for a given change in the input value (x).

Front

What is the graphical representation of a linear function?

Back

A linear function is represented by a straight line on a graph.

Front

What is the standard form of a linear function?

Back

The standard form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

What does it mean for a function to be nonlinear?

Back

A nonlinear function is one that does not create a straight line when graphed; it may curve or have varying slopes.

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input; this would violate the definition of a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value corresponds to one y-value.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 has two different outputs.