Understanding Function Values and Limits

The video tutorial explains how to evaluate the function value F(4) using a graph, identifying that F(4) equals 7 due to a plotted point. It then explores various limits: the one-sided limits as X approaches 1 from the right and left, showing different function values, and concludes that the overall limit as X approaches 1 does not exist. Finally, it evaluates the limit as X approaches 4, determining it exists and equals 5.

What is the function value of f(x) when x = 4?

• 3

• 9

• 5

• 7

What is the significance of a hole in the graph at x = 4?

• It means the function value is 7

• It suggests the limit does not exist

• It shows the function is undefined at that point

• It indicates the function value is zero

What is the function value of f(x) when x = 4, despite the hole in the graph?

• 9

• 7

• 5

• 3

When approaching x = 1 from the right, what value does the function approach?

• 4

• 3

• 2

• 1

What is the function value of f(x) when x = 1?

• 3

• 4

• 2

• 1

What does a one-sided limit from the right indicate?

• The average of the function values from both sides

• The behavior of the function as it approaches from the right

• The behavior of the function as it approaches from the left

• The function value at that point

When approaching x = 1 from the left, what value does the function approach?

• 1

• 4

• 3

• 2

Why does the limit as x approaches 1 not exist?

• The function value is zero at x = 1

• The function is undefined at x = 1

• The one-sided limits are different

• The graph has a hole at x = 1

What is the limit of f(x) as x approaches 4?

• 6

• 5

• 4

• 3

What does it mean if the limits from both sides of a point are equal?

• The function has a hole at that point

• The function value is zero

• The function is continuous at that point

• The limit does not exist