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; it indicates how much the output (y) changes for a unit change in the input (x).

Front

How do you find the slope from a linear equation in the form y = mx + b?

Back

The slope (m) is the coefficient of x in the equation.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

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

How can you determine which function has the greatest rate of change?

Back

The function with the highest absolute value of the slope has the greatest rate of change.

Front

What is the standard form of a linear function?

Back

The standard form of a linear function is Ax + By = C, where A, B, and C are constants.

Front

How do you compare two linear functions?

Back

You can compare two linear functions by examining their slopes and y-intercepts.

Front

What is the initial value of a function?

Back

The initial value is the output of the function when the input is zero, often represented by the y-intercept.