Periodic function ( period concavity average rate of change)

What is the period of a periodic function?

• The period of a periodic function is the value of x where f(x) = 0 for all x in the domain of the function.

• The period of a periodic function is the sum of all the values in the domain of the function.

• The period of a periodic function is the largest negative number T such that f(x+T) = f(x) for all x in the domain of the function.

• The period of a periodic function is the smallest positive number T such that f(x+T) = f(x) for all x in the domain of the function.

How can you determine the concavity of a function?

• Look at the first derivative of the function

• Find the second derivative of the function and analyze its sign to determine concavity.

• Analyze the function's domain

• Count the number of x-intercepts

Define the average rate of change of a function.

• The average rate of change of a function is the derivative of the function at a specific point.

• The average rate of change of a function is the total change in the function's output divided by the total change in the function's input over a specific interval.

• The average rate of change of a function is the maximum value of the function over a given interval.

• The average rate of change of a function is the slope of the tangent line to the function at a specific point.

If a function has a period of 2π, what is the length of one complete cycle?

• 2π

• 4π

• π

• 3π

How does the concavity of a function change at a point of inflection?

• The concavity remains the same at a point of inflection

• The concavity becomes undefined at a point of inflection

• The concavity oscillates at a point of inflection

• The concavity changes from positive to negative, or negative to positive, at a point of inflection.

Calculate the average rate of change of f(x) = 2x + 3 between x = 1 and x = 5.

• 4

• 2

• 5

• 10

Explain the concept of amplitude in a periodic function.

• The amplitude is the period of the function

• The amplitude in a periodic function is the distance between the maximum or minimum value and the average value of the function.

• The amplitude is the phase shift of the function

• The amplitude is the frequency of the function

What is the relationship between the period and frequency of a periodic function?

• Inverse proportionality

• Exponential relationship

• No relationship

• Direct proportionality

If a function is concave up, how does its graph look?

• The graph will have sharp spikes.

• The graph will be a straight line.

• The graph will be shaped like a smiley face, curving upwards.

• The graph will be shaped like a frown, curving downwards.

Find the average rate of change of g(x) = 3x^2 - 2x between x = -1 and x = 2.

• 7/3

• 4/3

• 5/3

• 2/3