Compare 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, indicating how much the output (y) changes for a unit change in the input (x).

Front

How do you find the slope from an equation in standard form (Ax + By = C)?

Back

Rearrange the equation to slope-intercept form (y = mx + b) to identify the slope (m).

Front

What is the rate of change in a linear function?

Back

The rate of change is the same as the slope and indicates how steep the line is.

Front

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

Back

By calculating the slopes of both functions and comparing their values.

Front

What does it mean if two functions have the same slope?

Back

It means they have the same rate of change and are parallel to each other.

Front

How do you determine which function is cheaper based on a cost equation?

Back

Substitute the same input value into both equations and compare the outputs.

Front

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

Back

The y-intercept is the value of the function when the input (x) is zero, indicating where the line crosses the y-axis.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b.

Front

How do you interpret a graph of a function?

Back

You analyze the slope, y-intercept, and overall shape to understand the relationship between the variables.