Nancy introduces the concept of limits, explaining how to read limit notation and interpret it on graphs. She discusses evaluating limits from both sides of a point, the significance of one-sided limits, and cases where limits do not exist. The video also covers limits as x approaches infinity, emphasizing the importance of understanding y-values in these contexts.

What does the limit of a function predict?

• The x-value the function approaches as y approaches a point

• The y-value the function approaches as x approaches a point

• The exact value of y at a point

• The slope of the function at a point

How do you read the notation 'lim x→1 f(x) = L'?

• The limit as y approaches L of f(x) equals 1

• The limit as x approaches L of f(x) equals 1

• The limit as x approaches 1 of f(x) equals L

• The limit as y approaches 1 of f(x) equals L

When finding a limit, why is it important to check values from both sides of a point?

• To ensure the function is continuous

• To determine the exact value of the function at that point

• To see if the y-values from both sides approach the same limit

• To find the slope of the function at that point

What does it mean if the left-hand limit and right-hand limit are equal?

• The function has a discontinuity at that point

• The overall limit exists and is equal to that value

• The function is undefined at that point

• The function is continuous at that point

If a function has a hole at x = 1 but approaches the same y-value from both sides, what is the limit as x approaches 1?

• The limit is undefined

• The limit is the x-value where the hole is

• The limit is the y-value the function approaches

• The limit does not exist

What is the significance of a point being defined above or below a hole in the context of limits?

• It makes the limit undefined

• It changes the limit value

• It does not affect the limit value

• It indicates a discontinuity

What does the notation 'lim x→2⁻ f(x)' represent?

• The limit as x approaches 2 from both sides

• The limit as x approaches 2 from the right

• The limit as x approaches 2 from the left

• The limit as x approaches -2

If the left-hand limit is 3 and the right-hand limit is 4, what can be said about the overall limit?

• The overall limit is 3

• The overall limit is 4

• The overall limit does not exist

• The overall limit is the average of 3 and 4

How do you determine the limit as x approaches infinity?

• By observing the y-value the function approaches as x increases

• By checking the function's behavior at x = 0

• By finding the exact value at infinity

• By finding the slope of the function as x increases

What is the limit as x approaches negative infinity if the function levels off at y = -1?

• The limit is infinity

• The limit does not exist

• The limit is -1

• The limit is 0