Increasing and Decreasing Functions

When is this function increasing?

• −2.5 < x < 2.5
• 0 < x < 5
• 0 < x < 55
• −5 < x < 0

Over what interval is this function constant?

• −5 < x < ∞
• −3 < x < 4
• 4 < x < ∞
• −5

List the types of intervals that the graph demonstrates in order.

• decreasing, constant, increasing, constant
• increasing, decreasing, constant
• increasing, constant, increasing, constant
• increasing, constant, decreasing, constant

Given a function, f(x), if f'(x)<0 over a certain interval, then f(x) is ____________ over that interval.

• decreasing
• increasing
• concave up
• concave down

What are the intervals on which f(x) = 2x⁴- 4x² + 1 is strictly increasing?

• (-1,0)

• (0,1)

• (-∞,-1) and (1,∞)

• (-1,0) and (1, ∞)

Let f be the function with derivative given by f'(x) = x² - 2/x.  On which of the following intervals is f decreasing?  (No Calculator)

• (-∞, 0]
• (-1, 0]
• (0, ∛2]
• (∛2, ∞)

If given f'(x) how would you find the intervals which the graph f(x) has a positive slope?

• f'(x) < 0 (negative)
• f'(x) > 0 (positive)
• f'(x) is increasing
• Can't be determined

When both the independent and dependent variables of a function increase across the entire domain, the function is called a...

• Increasing Function

• Decreasing Function

• Constant Function

When the dependent variable of a function decreases as the independent variable increases across the entire domain, the function is called a...

• Increasing Function

• Decreasing Function

• Constant Function

If the dependent variable of a function does not change or remains constant over the entire domain, then the function is called a...

• Increasing Function

• Decreasing Function

• Constant Function