Function Evaluation and Properties

Front

What is a function?

Back

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

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

How do you write a linear function?

Back

A linear function can be written in the form P(t) = mt + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

What is a linear equation?

Back

A linear equation is an equation that forms a straight line when graphed, typically in the form y = mx + b.

Front

What is the y-intercept?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if no two different inputs produce the same output.

Front

What is the significance of a function's graph?

Back

The graph of a function visually represents the relationship between the input and output values.

Front

How do you determine if a relation is a function?

Back

A relation is a function if every input has exactly one output; this can be checked using the vertical line test.