Comparing 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 the graph of a function represent?

Back

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

Front

What is the initial value of a function?

Back

The initial value of a function is the value of the function when the input is zero, often represented as the y-intercept on a graph.

Front

What does the rate of change in a function indicate?

Back

The rate of change indicates how much the output value of a function changes for a given change in the input value.

Front

How can you identify a function from a graph?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What does a flat section on a graph indicate?

Back

A flat section on a graph indicates that the output value is constant over that interval, meaning there is no change in output as the input changes.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions have varying rates of change and graph as curves.

Front

What is a slope in the context of a function?

Back

The slope of a function represents the rate of change of the output value with respect to the input value, calculated as the rise over run.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input values increase, the output values decrease.