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 is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise/run).

Front

What does the y-intercept represent in a graph?

Back

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

Front

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

Back

In the equation y = mx + b, 'm' represents the slope of the line.

Front

What is the difference between a positive slope and a 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

What is a linear function?

Back

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

Front

How can you determine if two functions are increasing or decreasing?

Back

A function is increasing if its slope is positive and decreasing if its slope is negative.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does it mean for two functions to have the same rate of change?

Back

Two functions have the same rate of change if they have the same slope.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates.