Functions and Limits Quiz

A function maps values from a set D (domain) to a unique element in set Y (range). What is the name given to the set of all possible values of f(x) as x varies throughout D?

• Domain

• Codomain

• Range

• Function

What defines a piecewise-defined function?

• It uses only one formula across its entire domain.

• It uses different formulas in different parts of its domain.

• It is always continuous.

• Its range is always a subset of its domain.

If f(-x) = f(x) for every x in the domain, the function is called:

• Odd

• Even

• Monotonic

• Piecewise

If f(-x) = -f(x) for every x in the domain, the function is called:

• Even

• Odd

• Monotonic

• Piecewise

A function is increasing if:

• f(x₁) > f(x₂) for x₁ < x₂

• f(x₁) < f(x₂) for x₁ < x₂

• f(x₁) = f(x₂) for x₁ < x₂

• f(x₁) ≥ f(x₂) for x₁ < x₂

A function is decreasing if:

• f(x₁) < f(x₂) for x₁ < x₂

• f(x₁) > f(x₂) for x₁ < x₂

• f(x₁) = f(x₂) for x₁ < x₂

• f(x₁) ≤ f(x₂) for x₁ < x₂

Which of the following is NOT a type of function mentioned in the document?

• Hyperbolic

• Exponential

• Polynomial

• Trigonometric

• Power

The composition of functions f and g, denoted as (f ∘ g)(x), is defined as:

• f(x) + g(x)

• f(x) * g(x)

• f(g(x))

• g(f(x))

What condition must be met for the limit of f(x) as x approaches 'a' to be 'L'?

• f(a) = L

• For any ε > 0, there exists a δ > 0 such that 0 < |x - a| < δ implies |f(x) - L| < ε.

• f(x) is continuous at x = a

• f(x) is differentiable at x = a

What is a one-sided limit?

• A limit that only considers values of x approaching 'a' from one direction (either left or right).

• A limit that is always equal to the function's value at the point.

• A limit that does not exist.

• A limit that is always infinite.