Question

What is the difference between an excluded value and a hole?

a) An excluded value is a point where the function is undefined, while a hole is a missing point in the graph.
b) An excluded value is a missing point in the graph, while a hole is a point where the function is undefined.
c) Both excluded values and holes represent points where the function is undefined.
d) Excluded values and holes are interchangeable terms, referring to the same mathematical concept.

Answer 1

An excluded value is a point where the function is undefined, while a hole is a missing point in the graph.

Step-by-step explanation:

An excluded value is a point where the function is undefined, while a hole is a missing point in the graph.

For example, let's consider the rational function f(x) = (x^2 - 4)/(x - 2).

At x = 2, the denominator becomes 0, which makes the function undefined. This is an excluded value. On the graph, there is a hole at x = 2, where the point (2, 4) is missing.

Therefore, option a) is correct - an excluded value is a point where the function is undefined, while a hole is a missing point in the graph.