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 is the rate of change in a function?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity, often represented as the slope in a linear function.

Front

What is the initial value of a function?

Back

The initial value is the output of the function when the input is zero, representing the starting point of the function.

Front

How do you identify the fastest growing function?

Back

To identify the fastest growing function, compare the rates of change (slopes) of the functions; the one with the highest rate of change grows the fastest.

Front

What does a positive rate of change indicate?

Back

A positive rate of change indicates that as the input increases, the output also increases.

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that as the input increases, the output decreases.

Front

How can you represent a function graphically?

Back

A function can be represented graphically using a coordinate plane, where the x-axis represents the input and the y-axis represents the output.

Front

What is a linear function?

Back

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

Front

What is the slope of a line?

Back

The slope of a line is the ratio of the rise (change in y) to the run (change in x), indicating the steepness and direction of the line.

Front

What is the y-intercept of a function?

Back

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