Writing Function Rules

Front

What is a function rule?

Back

A function rule is an equation that describes the relationship between input (independent variable) and output (dependent variable) in a function.

Front

How do you represent a function in a table?

Back

A function can be represented in a table by listing pairs of input values and their corresponding output values.

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if every input value (x-coordinate) corresponds to exactly one output value (y-coordinate), which can be tested using the vertical line test.

Front

What is the vertical line test?

Back

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

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; it shows how much the output value changes for a unit change in the input value.

Front

What is the y-intercept in a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the output value when the input value is zero.

Front

How do you write a function rule from a word problem?

Back

To write a function rule from a word problem, identify the variables involved, determine how they relate to each other, and express this relationship as an equation.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the input of the function (often represented as x), while the dependent variable is the output (often represented as y) that depends on the input.

Front

How can you identify a function from a set of ordered pairs?

Back

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