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 function represent?

Back

The slope of a function 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 two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the function crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

How can you compare the slopes of two functions?

Back

You can compare the slopes by calculating the slope of each function and determining which is greater, less than, or equal.

Front

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

Back

If two functions have the same slope, they are parallel and will never intersect, indicating they have the same rate of change.

Front

How do you determine which function is cheaper based on their equations?

Back

To determine which function is cheaper, substitute the same input value into both equations and compare the outputs.

Front

What is the significance of the coefficients in a linear function?

Back

The coefficients in a linear function determine the slope and y-intercept, affecting the steepness and position of the line on a graph.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, typically represented in the form y = mx + b.

Front

How do you interpret the meaning of a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in the output regardless of the input.