Increasing Decreasing Functions

Where is the function increasing?

• [4, ∞)

• [−4, ∞)

• [6, ∞)

• 4 < x < 6

Tags

CCSS.HSF-IF.C.7A

Where is the decreasing?

• ( −∞, −2.55) U (0, 2.55)

• (∞, −6.25) U (36, −6.25)

• (−∞, ∞)

• (−∞, 0)

Where is the function increasing?

• y ≥ −1

• y ≤ −1

• y ≥ 3

• y ≤ 3

Tags

CCSS.HSF-IF.C.7A

• x = 2
• x = 1
• x = −1
• No Absolute Minimum

What is the absolute max?

• (0, 36)

• (−2.55, −6.55), (2.55, −6.55)

• (−∞, ∞)

• None

Tags

CCSS.HSF-IF.C.7A

What is the domain of the graph?

• -7 ≤ x < 5

• -3 ≤ x < 1

• -3 ≤ y < 1

• -7 ≤ y < 5

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

f is increasing on the interval 2 < x < 9 because for all a and b in the interval, if
a < b,
then...

• f(9) > f(2)

• f(a) < f(b)

• f(a) > f(b)

• f(2) < f(9)

Categorize the following function from (B,C).

• Increasing with an increasing rate of change

• Increasing with a constant rate of change

• Decreasing with an increasing rate of change

• Decreasing with a decreasing rate of change

Answer explanation

Remember! Where the function is linear, the rate of change is constant (a positive constant slope, negative constant slope, or zero slope)

Tags

CCSS.HSF.IF.B.4

If a function is increasing on [x1, x2]

• The rate of change is positive on [x1, x2]

• The rate of change is negative on [x1, x2]

• f(x1) < f(x2) for all x on the interval [x1, x2], where x1 < x2

• f(x1)>f(x2) for all x on the interval [x1, x2], where x1 < x2

True or false: A function can either be only decreasing or only increasing on a given interval

• TRUE

• FALSE