Comparing Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as an equation, a graph, or a table.

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. In linear functions, it is represented by the slope.

Front

How do you find the slope of a line?

Back

The slope (m) is calculated as the change in y divided by the change in x (m = Δy/Δx).

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases.

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

How can you determine if two functions have the same rate of change?

Back

Two functions have the same rate of change if their slopes are equal.

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 (x=0).

Front

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

Back

To compare rates of change, calculate the slope of each function and compare the values.

Front

What is a linear function?

Back

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