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 rate of change in a function represent?

Back

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

Front

How do you identify the initial value in a linear function?

Back

The initial value is the y-intercept of the function, which is the value of y when x is 0.

Front

What is the difference between a linear function and a non-linear function?

Back

A linear function has a constant rate of change and graphs as a straight line, while a non-linear function has a variable rate of change and graphs as a curve.

Front

How can you determine which function has the greatest initial value?

Back

Compare the y-intercepts of the functions; the function with the highest y-intercept has the greatest initial value.

Front

What does a graph showing a flat line indicate about a function?

Back

A flat line indicates that the function's output is constant over that interval, meaning there is no change in output as the input changes.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; a positive slope means the function is increasing, while a negative slope means it is decreasing.

Front

How do you find the slope of a line given two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the two points.

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.