1.2 Rate of Change

Which of the following statements is true about a function with a negative rate of change?

• The function is always increasing
• The function is always concave down
• The function is always concave up
• The function is always decreasing

Which of the following is NOT a correct statement about rate of change?

• Rate of change can be positive or negative, increasing or decreasing
• Rate of change can only be calculated using the formula
• Rate of change is essentially slope
• Rate of change is classified as positive or negative and increasing or decreasing

Which of the following statements is true about inflection points?

• They are points where concavity changes
• They are points where the rate of change is zero
• They have no impact on concavity
• They only occur on linear functions

Which of the following statements is true about a function with an increasing rate of change?

• The function is always concave down
• The function is always increasing
• The function is always concave up
• The function is always decreasing

What does a decreasing rate of change indicate about a function?

• The function is increasing
• The function is concave up
• The function is decreasing
• The function is concave down

What is the formula for calculating rate of change?

• Change in x times change in y
• Change in x over change in y
• Change in y times change in x
• Change in y over change in x

What does a positive rate of change indicate about a function?

• The function is decreasing
• The function is concave up
• The function is increasing
• The function is concave down

What is the relationship between rate of change and the direction of a function?

• Rate of change and direction of a function are unrelated
• Rate of change and direction of a function change at an inflection point
• A positive rate of change means the function is increasing, while a negative rate of change means the function is decreasing
• A positive rate of change means the function is concave up, while a negative rate of change means the function is concave down

What is the relationship between rate of change and concavity?

• Rate of change and concavity are unrelated
• Rate of change is always negative when the function is concave down
• Rate of change is always positive when the function is concave up
• Rate of change and concavity change at an inflection point