Exploring Increasing and Decreasing Intervals of Functions

What do the terms 'increasing' and 'decreasing' refer to in the context of a function?

• The intercepts of the function

• The x-values of the function

• The y-values of the function

• The slope of the function

How are intervals always read?

• Right to left

• Top to bottom

• Left to right

• Bottom to top

What is the general behavior of the function x^3 + 3x^2 - 1?

• Decreasing, then increasing, then decreasing

• Increasing, then decreasing, then increasing

• Always increasing

• Always decreasing

At which x-value does the function stop increasing for the first time?

• x = 2

• x = -1

• x = -2

• x = 0

From which x-values does the function start decreasing?

• x = -2 to x = 0

• x = 0 to x = 2

• x = 1 to x = 3

• x = -3 to x = -1

What is the interval notation for the function increasing from negative infinity to x = -2?

• (-∞, 0)

• (-2, 0)

• (-∞, -2)

• (0, ∞)

What is the interval notation for the function increasing from x = 0 to positive infinity?

• (-∞, 0)

• (-2, 0)

• (0, ∞)

• (-∞, -2)

What is the interval notation for the function decreasing from x = -2 to x = 0?

• (-∞, 0)

• (0, ∞)

• (-2, 0)

• (-∞, -2)

Why do we use parentheses to denote the endpoints of intervals?

• To include the endpoints

• To exclude the endpoints

• For convention, without specifying inclusion or exclusion

• To denote open intervals

What is the overall behavior of the function from negative infinity to positive infinity?

• Increasing, decreasing, then increasing

• Decreasing, increasing, then decreasing

• Always increasing

• Always decreasing