Increasing Decreasing Functions

Where is the function increasing?

• [4, ∞)

• [−4, ∞)

• [6, ∞)

• 4 < x < 6

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

• 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

What is the domain of the graph?

• -7 ≤ x < 5

• -3 ≤ x < 1

• -3 ≤ y < 1

• -7 ≤ y < 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)

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