Compare Functions (2)

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values (x) increase, the output values (y) also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input values (x) increase, the output values (y) decrease.

Front

How can you determine if a function is increasing or decreasing from a graph?

Back

If the graph rises from left to right, the function is increasing. If it falls from left to right, the function is decreasing.

Front

What is an initial value of a function?

Back

The initial value of a function is the value of the function when the input (x) is zero.

Front

How do you compare the initial values of two functions?

Back

You compare the initial values by evaluating both functions at x=0 and determining which is greater.

Front

What is the rate of change in a function?

Back

The rate of change is the ratio of the change in the output value to the change in the input value, often represented as the slope of the function.

Front

How can you determine the rate of change from a graph?

Back

The rate of change can be determined by calculating the slope of the line connecting two points on the graph.

Front

What does it mean if two functions have the same rate of change?

Back

If two functions have the same rate of change, they are parallel and will never intersect.

Front

What does it mean for a function to be steeper?

Back

A function is steeper if it has a greater rate of change, meaning it rises or falls more sharply.

Front

How can you tell if two functions have different rates of change?

Back

You can tell if two functions have different rates of change by comparing their slopes; if the slopes are different, the rates of change are different.