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?

Back

The slope of a line represents the rate of change of the function, indicating how much the output (y) changes for a given change in the input (x).

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented as (0, y).

Front

How can you determine the y-intercept from a linear equation in slope-intercept form?

Back

In the slope-intercept form y = mx + b, the y-intercept is the value of b.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, which can be expressed in the form y = mx + b.

Front

What is the difference between a positive and negative slope?

Back

A positive slope indicates that as x increases, y also increases, while a negative slope indicates that as x increases, y decreases.

Front

How do you compare the rates of change of two functions?

Back

You compare the slopes of the functions; the function with the greater slope has a higher rate of change.

Front

What is a table of values in relation to functions?

Back

A table of values lists pairs of input (x) and output (y) values for a function, helping to visualize the relationship.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input (x) increases, the output (y) also increases.