Exploring Function Intervals: Increasing, Decreasing, Positive, and Negative

What does it mean for a function to be positive?

• The function is decreasing.

• The function is increasing.

• The function is above the x-axis.

• The function is below the x-axis.

If a function is positive between x = a and x = b, what can be said about the function at x = a and x = b?

• The function is undefined at x = a and x = b.

• The function is zero at x = a and x = b.

• The function is negative at x = a and x = b.

• The function is positive at x = a and x = b.

In which interval is the function negative if x is between b and c?

• The function is undefined.

• The function is negative.

• The function is zero.

• The function is positive.

What does it mean for a function to be increasing?

• As x increases, y remains constant.

• As x increases, y increases.

• As x decreases, y increases.

• As x increases, y decreases.

At which points is the function neither increasing nor decreasing?

• At points where the slope of the tangent line is negative.

• At points where the slope of the tangent line is positive.

• At points where the slope of the tangent line is undefined.

• At points where the slope of the tangent line is zero.

If x is less than d, what can be said about the function?

• The function is undefined.

• The function is zero.

• The function is increasing.

• The function is decreasing.

What happens to y as x increases between d and e?

• y becomes undefined.

• y decreases.

• y remains constant.

• y increases.

In which interval is the function decreasing?

• For x less than d.

• For x equal to d or e.

• For x greater than e.

• For x between d and e.

What is the relationship between positive/negative intervals and increasing/decreasing intervals?

• They always coincide.

• They never coincide.

• They sometimes coincide.

• They are unrelated.

Why is it important to consider positive/negative intervals and increasing/decreasing intervals separately?

• Because they always coincide.

• Because they are unrelated.

• Because they never coincide.

• Because they sometimes coincide but are not the same.