Comparing Functions L17/L18 Flashcard

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval 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 on an interval if, as the input values increase, the output values decrease.

Front

What is a constant function?

Back

A constant function is a function that does not change its value; it remains the same for all inputs.

Front

How can you identify intervals of increase and decrease on a graph?

Back

Intervals of increase and decrease can be identified by observing the slope of the graph: rising slopes indicate increasing intervals, while falling slopes indicate decreasing intervals.

Front

What is the significance of the y-intercept in a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the output value when the input is zero.

Front

How do you determine the average rate of change of a function?

Back

The average rate of change of a function over an interval is calculated by taking the difference in output values divided by the difference in input values.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not graph to a straight line, such as quadratic or exponential functions.

Front

What does it mean for two functions to be equivalent?

Back

Two functions are equivalent if they produce the same output for every input in their domain.