Exploring Infinite Limits as x Approaches a

Mr. Baker explains infinite limits, focusing on how functions behave as x approaches a specific value. He uses the function f(x) = 1/x to demonstrate graphically what happens as x approaches 0, highlighting the concept of vertical asymptotes. The video further explores finding vertical asymptotes for the function f(x) = 1/(x-2), describing the behavior of the graph on both sides of the asymptote. The video concludes with a summary of these concepts.

What happens to the values of a function as x approaches a specific value, in terms of infinity?

• They remain unchanged.

• They grow boundlessly, either towards positive or negative infinity.

• They approach a constant value.

• They oscillate between positive and negative values.

Why can't we plug 0 into the function f(x) = 1/x?

• Because it eliminates the variable x.

• Because it results in an undefined value.

• Because it makes the function linear.

• Because it turns the function into a constant.

What is observed when approaching 0 from the right hand side on the graph of f(x) = 1/x?

• The graph oscillates.

• The graph goes up to positive infinity.

• The graph remains constant.

• The graph goes down to negative infinity.

What is the behavior of the graph of f(x) = 1/x as it approaches 0 from the left hand side?

• It goes down to negative infinity.

• It oscillates.

• It remains constant.

• It goes up to positive infinity.

What does the presence of a vertical asymptote indicate about a graph?

• The graph touches the x-axis at that point.

• The graph extends to positive or negative infinity as it approaches that point.

• The graph becomes linear at that point.

• The graph becomes undefined at that point.

What general condition indicates the presence of a vertical asymptote in a function's graph?

• The function touches the x-axis at that point.

• The function's limit approaches a constant value as x approaches that point.

• The function becomes linear at that point.

• The function's limit approaches positive or negative infinity as x approaches that point.

For the function f(x) = 1/(x - 2), where is the vertical asymptote located?

• x = 2

• x = 1

• x = 3

• x = 0

What behavior is observed as x approaches 2 from the left hand side for f(x) = 1/(x - 2)?

• The graph goes down to negative infinity.

• The graph goes up to positive infinity.

• The graph remains constant.

• The graph oscillates.

Why is 2 not in the domain of the function f(x) = 1/(x - 2)?

• Because it eliminates the variable x.

• Because it turns the function into a constant.

• Because it results in a division by zero.

• Because it makes the function linear.

What is the limit of f(x) = 1/(x - 2) as x approaches 2 from the right hand side?

• Positive infinity

• Negative infinity

• Undefined

• 0