Interpreting & Sketching Functions

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 does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, meaning it has a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line, indicating that the rate of change is not constant.

Front

How can you determine if a table of values represents a linear function?

Back

If the differences between consecutive outputs (y-values) are constant for equal intervals of inputs (x-values), the function is linear.

Front

What does a constant speed graph look like?

Back

A constant speed graph is a straight line that slopes upwards or downwards, indicating uniform motion.

Front

What does an acceleration graph represent?

Back

An acceleration graph shows a curve that indicates the speed of an object is changing over time.

Front

What does a graph that is flat (horizontal) indicate?

Back

A flat graph indicates that the object is not moving; its position remains constant over time.

Front

What is the significance of the slope in a function's graph?

Back

The slope represents the rate of change of the function; a steeper slope indicates a greater rate of change.

Front

What does it mean for a graph to increase?

Back

A graph is increasing when the y-values rise as the x-values increase.

Front

What does it mean for a graph to decrease?

Back

A graph is decreasing when the y-values fall as the x-values increase.