Precalculus - functions

If a function has a slope that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The concavity of the function is up
• The concavity of the function is down

When the rate of change of f(x) changes from positive to negative, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

Find the intervals of concavity for

f(x) = x² + 2x + 1.

• concave up: (-∞,∞)

• concave down: (-∞,∞)

• concave up: (2, ∞)

  concave down: (-∞,2)

• concave up: (-∞,2)

  concave down: (2, ∞)

When the rate of change of f(x) changes from positive to negative, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

Where is the function decreasing?

• (-∞, -1)
• (-1, ∞)
• (-∞, 3)
• (-∞, ∞)

When is this function increasing?

• (-3, 3)

• (-2.5, 2.5)

• [-3, 3]

• (3, ∞)

When is this function decreasing?

• (-3, 3)

• (-∞, -3) U (3, ∞)

• (-∞, -3] U [3, ∞)

• [-3, 3]

On which interval(s) is the given function increasing?

• (-∞, 2) U (-2, ∞)

• (-2, 2) U (-2, ∞)

• (-∞, -2) U (0.5, ∞)

• (0, 2) U (0.5, ∞)

Describe the interval(s) over which the given function is decreasing.

• (-∞, 0) U (2, ∞)

• (5, -4) U (0, -3)

• (-3, 0) U (2, 3)

• (2, 3)

concavity

• concave up only

• concave down only

• both concave up and down

• none