Understanding Limits from a Graph

The video tutorial explains how to determine four different limits using a provided graph. It covers the process of evaluating limits as X approaches specific values, including the use of absolute values. The tutorial emphasizes understanding the behavior of functions from both the right and left sides, ensuring that the limits exist and are equal. Each example is broken down step-by-step to illustrate the concept of limits and how they are calculated.

What is the limit of f(x) as x approaches 1?

• 1

• 2

• 0

• 3

As x approaches 1 from both sides, what value does the function approach?

• 3

• 0

• 1

• 2

What is the limit of f(x + 1) as x approaches 2?

• 2

• 4

• 1

• 3

When x approaches 2, what input value does f(x + 1) approach?

• 4

• 3

• 2

• 5

What is the limit of f(2x - 4) as x approaches 3?

• -1

• -2

• 1

• 0

As x approaches 3, what input value does f(2x - 4) approach?

• 2

• 1

• 4

• 3

What is the limit of |f(4 + x)| as x approaches 0?

• 2

• 3

• 1

• 0

Why does the limit of |f(4 + x)| exist as x approaches 0?

• Because the input approaches 0

• Because the function is continuous

• Because the absolute value makes the one-sided limits equal

• Because the function is differentiable

What would happen to the limit of f(4 + x) as x approaches 0 if there was no absolute value?

• The limit would still exist

• The limit would be infinite

• The limit would be zero

• The limit would not exist

As x approaches 0, what input value does f(4 + x) approach?

• 6

• 3

• 4

• 5