How to find the limits of a piecewise function by graphing first

The video tutorial explains how to graph functions and understand restrictions. It covers the concept of left and right hand limits, demonstrating how to evaluate them using graphs. The tutorial also discusses when a general limit does not exist. Finally, it introduces a similar problem involving absolute values and exponentials.

What is the purpose of graphing a function when analyzing its behavior?

• To find the exact values of x and y

• To calculate the area under the curve

• To understand the function's behavior and restrictions

• To determine the function's derivative

When approaching a point from the left on a graph, what are we trying to determine?

• The area under the curve

• The x-value at that point

• The slope of the tangent line

• The y-value the function approaches

How can you find the left-hand limit of a function algebraically?

• By finding the average of the function values

• By plugging the point into the top equation

• By integrating the function

• By differentiating the function

What is the right-hand limit of a function?

• The integral of the function from a point to infinity

• The value the function approaches as x approaches a point from the right

• The average value of the function over an interval

• The derivative of the function at a point

Under what condition does a general limit not exist?

• When the left and right-hand limits are equal

• When the function is differentiable

• When the function is continuous

• When the left and right-hand limits are not equal