Interpreting Graphs of Functions Section 4.5

Front

What is a function in mathematics?

Back

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

Front

What does a graph represent in the context of functions?

Back

A graph visually represents the relationship between the input (x-axis) and output (y-axis) of a function.

Front

What does it mean when a graph is flat (horizontal)?

Back

A flat graph indicates that the output value is constant, meaning the object is not moving.

Front

What does a rising graph indicate?

Back

A rising graph indicates that the output value is increasing, meaning the object is moving away from the starting point.

Front

What does a falling graph indicate?

Back

A falling graph indicates that the output value is decreasing, meaning the object is moving back towards the starting point.

Front

What does it mean when a graph has a steep slope?

Back

A steep slope indicates that the object is moving quickly.

Front

What does it mean when a graph has a gentle slope?

Back

A gentle slope indicates that the object is moving slowly.

Front

What does a vertical line on a graph represent?

Back

A vertical line indicates that the input value is constant while the output value changes, which is not a function.

Front

What is the significance of points on a graph?

Back

Points on a graph represent specific values of the function at given inputs.

Front

What does it mean when a graph shows a curve?

Back

A curve indicates that the rate of change of the output is not constant; the object may be speeding up or slowing down.