FAC Calculus Unit 1 Limits and Continuity

What is the definition of a Limit?

• A line that a graph approaches but never touches

• The slope of a tangent line to a curve

• The value that a function approaches as the input approaches some value

• The output values of a function

What does the term "Instantaneous Rate of Change" refer to?

• The average change in a function over an interval

• The change in a function at a specific point

• The total change in a function over time

• The slope of a secant line

What is the "Average Rate of Change"?

• The change in a function at a specific point

• The total change in a function over time

• The change in a function over an interval

• The slope of a tangent line

What is an "Asymptote"?

• A line that a graph approaches but never touches

• The slope of a tangent line to a curve

• The value that a function approaches as the input approaches some value

• The output values of a function

What is "Continuity" in a function?

• The function has no breaks, jumps, or holes

• The function has a vertical asymptote

• The function has a horizontal asymptote

• The function has a jump discontinuity

What is the "Intermediate Value Theorem"?

• If a function is continuous on [a, b], then it takes on every value between f(a) and f(b)

• If a function is differentiable, it has a tangent line at every point

• If a function has a limit, it is continuous

• If a function is increasing, it has a maximum value

What is the Instantaneous Rate of Change?

• The total distance traveled divided by the total time

• The slope of the secant line between two points on a curve

• The slope of the tangent line to a curve at a specific point

• The overall change in a function over a given interval

The Average Rate of Change of a function over an interval is:

• The slope of the tangent line at a point

• The total change in the function's value divided by the change in the input

• The value a function approaches as the input approaches some value

• The initial value of a function

Average velocity is defined as:

• The instantaneous speed at a specific moment

• The change in position over time for a specific interval

• The slope of the curve at a particular point

• The total displacement divided by the total time taken

An Interval refers to:

• A specific point on a graph

• The difference between two points

• A set of numbers between two endpoints

• The slope of a line