1.1-1.3 Extra Practice

Front

What is the rate of change of a function?

Back

The rate of change of a function measures how the output value of the function changes as the input value changes. It is often represented as the slope of the function's graph.

Front

Define positive rate of change.

Back

A positive rate of change indicates that as the input (x) increases, the output (f(x)) also increases.

Front

Define negative rate of change.

Back

A negative rate of change indicates that as the input (x) increases, the output (f(x)) decreases.

Front

What does it mean for a function to be increasing at a decreasing rate?

Back

A function is increasing at a decreasing rate when the slope of the function is positive but getting smaller, indicating that the function is rising but at a slower pace.

Front

What does it mean for a function to be decreasing at an increasing rate?

Back

A function is decreasing at an increasing rate when the slope of the function is negative and becoming more negative, indicating that the function is falling faster.

Front

What is concavity in relation to a function's graph?

Back

Concavity refers to the direction of the curvature of a graph. A graph is concave up if it opens upwards (like a cup) and concave down if it opens downwards.

Front

What does it mean for a function to be concave up?

Back

A function is concave up if its second derivative is positive, indicating that the rate of change of the function is increasing.

Front

What does it mean for a function to be concave down?

Back

A function is concave down if its second derivative is negative, indicating that the rate of change of the function is decreasing.

Front

How can you determine if a function is increasing or decreasing from its graph?

Back

A function is increasing where the graph rises from left to right and decreasing where the graph falls from left to right.

Front

What is the significance of intervals in analyzing functions?

Back

Intervals help identify where a function is increasing, decreasing, or constant, and are crucial for understanding the behavior of the function.