Compare Functions (2)

Front

What is an increasing function?

Back

A function is increasing if, for any two points x1 and x2 in its domain, if x1 < x2, then f(x1) < f(x2).

Front

What is a decreasing function?

Back

A function is decreasing if, for any two points x1 and x2 in its domain, if x1 < x2, then f(x1) > f(x2).

Front

How do you determine the rate of change of a linear function?

Back

The rate of change of a linear function can be found using the formula: \( \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} \) 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 the function is increasing as you move from left to right on the graph.

Front

What does a negative slope indicate about a function?

Back

A negative slope indicates that the function is decreasing as you move from left to right on the graph.

Front

What is the slope of the line passing through points (0, 2) and (2, 6)?

Back

The slope is 2, calculated as \( \frac{6 - 2}{2 - 0} = 2 \).

Front

What is the significance of the steepness of a line?

Back

The steepness of a line, or its slope, indicates the rate of change of the function; a steeper line has a greater rate of change.

Front

How can you compare the slopes of two linear functions?

Back

You can compare the slopes by calculating each slope using the formula \( \frac{y_2 - y_1}{x_2 - x_1} \) and comparing the resulting values.

Front

What does it mean if two lines have the same steepness?

Back

If two lines have the same steepness, they have the same slope, indicating they change at the same rate.

Front

What is the formula for the slope of a line?

Back

The formula for the slope (m) of a line is: \( m = \frac{y_2 - y_1}{x_2 - x_1} \).