Functions and Rate of Change

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the rate of change?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity, often expressed as a ratio.

Front

How do you write a linear equation for a situation?

Back

Identify the fixed cost and the variable cost, then use the formula y = mx + b, where m is the rate of change and b is the initial value.

Front

What does the slope of a line represent in a graph?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable.

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

How can 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 on a graph.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.

Front

What does 'y = mx + b' represent?

Back

This is the slope-intercept form of a linear equation, where m is the slope and b is the y-intercept.

Front

What is a constant rate of change?

Back

A constant rate of change means that the change in the output value is the same for every unit change in the input value.