Key Features of Functions

Front

What are the intervals where a function is positive?

Back

The function is positive in the intervals where its output values are greater than zero.

Front

What are the intervals where a function is negative?

Back

The function is negative in the intervals where its output values are less than zero.

Front

How do you determine where a function is increasing?

Back

A function is increasing on intervals where the output values rise as the input values increase.

Front

How do you determine where a function is decreasing?

Back

A function is decreasing on intervals where the output values fall as the input values increase.

Front

What are x-intercepts of a function?

Back

X-intercepts are points where the function crosses the x-axis, meaning the output value is zero.

Front

What are y-intercepts of a function?

Back

Y-intercepts are points where the function crosses the y-axis, meaning the input value is zero.

Front

What does it mean for a function to be positive on an interval?

Back

It means that for every x-value in that interval, the function's output is greater than zero.

Front

What does it mean for a function to be negative on an interval?

Back

It means that for every x-value in that interval, the function's output is less than zero.

Front

What is the significance of critical points in a function?

Back

Critical points are where the function's derivative is zero or undefined, indicating potential maxima, minima, or points of inflection.

Front

How can you find the intervals of increase and decrease using the first derivative?

Back

By analyzing the sign of the first derivative; if it's positive, the function is increasing; if negative, it's decreasing.