Positive or Negative Intervals

Front

What is a positive interval in a function?

Back

A positive interval is a range of values for which the function's output is greater than zero.

Front

What is a negative interval in a function?

Back

A negative interval is a range of values for which the function's output is less than zero.

Front

How do you determine if a function is positive or negative over an interval?

Back

Evaluate the function at points within the interval. If the output is greater than zero, the function is positive; if less than zero, it is negative.

Front

What does the notation (a, b) represent?

Back

It represents an open interval from a to b, meaning a and b are not included in the interval.

Front

What does the notation [a, b] represent?

Back

It represents a closed interval from a to b, meaning a and b are included in the interval.

Front

What is the significance of critical points in determining intervals?

Back

Critical points are where the function changes from positive to negative or vice versa, helping to identify positive and negative intervals.

Front

If a function is positive on (0, ∞), what does this imply?

Back

It implies that for all values greater than 0, the function's output is positive.

Front

If a function is negative on (-∞, 0), what does this imply?

Back

It implies that for all values less than 0, the function's output is negative.

Front

What is the union of intervals, such as (-4, 2) U (5, ∞)?

Back

It represents all values in both intervals combined, meaning the function is positive in both ranges.

Front

How can you graphically represent positive and negative intervals?

Back

On a number line, shade the regions corresponding to positive intervals and leave the negative intervals unshaded.