8.5 Continuity mastery practice

What is the first step to determine if a function is continuous at a point?

• Evaluate f(a) where 'a' is the input

• Check if the function is polynomial

• Graph the function to observe continuity

• Calculate the derivative of the function

What should you do if the limit of the function as x approaches a specific point exists?

• Ignore it as it is not necessary

• Calculate the integral of the function

• Compare it to the function's output at that point

• Conclude the function is always continuous

What indicates a function is discontinuous at a point?

• The function's output equals the limit

• The limit does not exist

• The derivative at that point is zero

• The function is non-linear

In the example, what is the value of f(1) for the function f(x) = 2x?

• 2

• 3

• 0

• 1

If f(a) and the limit as x approaches a are the same, the function is:

• Continuous

• Discontinuous

• Non-differentiable

• Undefined

• None of the above.

Answer explanation

From the left, the limit is 4 and from the right, the limit is -3. So, both of those one-sided limits, but since they are not equal, the two-sided limit does not exist.

• None of the above.

Answer explanation

From the left, the limit is 1 and from the right the limit is -4. Since it is a closed point at (2,-4), the function is also defined at x=2. But, since the left and right limits are not equal, the limit does not exist.

• None of the above.

Answer explanation

Since both left and right limits are 1, the limit exists. But, since it is a open point, the point is not defined.

• None of the above.

Answer explanation

• Yes

• No