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 function represent?

Back

The slope 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 y-intercept of a function?

Back

The y-intercept is found by setting x to 0 in the function's equation and solving for y.

Front

What is the formula for the slope of a line?

Back

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

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

What is the difference between a linear function and a non-linear function?

Back

A linear function has a constant rate of change and can be represented by a straight line, while a non-linear function has a variable rate of change and is represented by a curve.

Front

How can you determine which function has a greater rate of change?

Back

You can compare the slopes of the functions; the function with the larger slope has a greater rate of change.

Front

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

Back

The y-intercept is the point where the function crosses the y-axis, representing the output value when the input is zero.

Front

How do you compare the y-intercepts of two functions?

Back

Evaluate both functions at x = 0 and compare the resulting y values.