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 slope of a line represent in a function?

Back

The slope represents the rate of change of the function; it indicates how much the output (y) changes for a unit change in the input (x).

Front

How do you determine which function grows faster?

Back

Compare the slopes of the functions; the function with the greater slope grows faster.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate about a function?

Back

A positive slope indicates that as the input (x) increases, the output (y) also increases.

Front

What does a negative slope indicate about a function?

Back

A negative slope indicates that as the input (x) increases, the output (y) decreases.

Front

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

Back

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

Front

How can you tell if two functions have the same slope?

Back

If the coefficients of x in their equations are equal, then they have the same slope.

Front

What does it mean for two functions to be parallel?

Back

Two functions are parallel if they have the same slope but different y-intercepts.

Front

What is the rate of change in a function?

Back

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