Graphing functions

Increasing interval?

• Where the graph goes up

• Where the graph is going down

• The middle of the graph

Which of the following is the decreasing interval of the function?

• $\left(-\infty,1\right)$

• $\left(1,\infty\right)$

• $\left(-\infty,-1\right)$

• $\left(-1,\infty\right)$

State the interval of decreasing.

• (-2, ∞)

• (-∞, -2)

• (-∞, ∞)

• None

Where is the function decreasing?

• A

  (−∞ < x < −2.55) U (0 ≤ x ≤ 2.55)

• B

  (∞ < x < −6.25) U (36 < x < −6.25)

• C

  −∞ < x < ∞

• D

  −∞ < x < 0

• Increasing

• Decreasing

• Constant

Which coordinate would qualify as the *absolute maximum* of this function?

• ∞

• (0, 4)

• 3

• (4, 0)

Is the highlighted section of the graph increasing, decreasing or no change?

• increasing

• decreasing

• no change

Which functions have a relative maximum value?

• 
• 
• 
• 

Over what interval is the function shown in the table decreasing? Use no spaces in your answer. Only use numbers and inequality signs.

Answer explanation

The parabola is opened upwards since a = 3. Although it is more narrow than the parent function, it is still decreasing on the interval

(-infinity, 0). Since we read from left to right, as we look at x values that are less than 0, as we get closer and closer to 0 the y values decrease. Therefore the interval x<0 is decreasing and x>0 is increasing.

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, ∞)