Function Concepts Quiz

A function maps values from a set D (domain) to a unique element in set Y (range). What does D represent?

• The range of the function

• The set of all possible output values

• The set of all possible input values

• The graph of the function

A piecewise-defined function is:

• Always continuous

• Defined by different formulas in different parts of its domain

• Always linear

• Never differentiable

An even function satisfies which condition?

• f(-x) = -f(x)

• f(-x) = f(x)

• f(x) = x

• f(x) = 0

What describes a function increasing on an interval I?

• f(x₁) > f(x₂) for any x₁ < x₂ in I

• f(x₁) < f(x₂) for any x₁ < x₂ in I

• f(x₁) = f(x₂) for any x₁ < x₂ in I

• f(x) is constant on I

What is the degree of the polynomial P(x) = 3x⁵ - 2x² + 7?

• 2

• 3

• 5

• 7

A rational function is defined as:

• f(x) = ax + b

• f(x) = ax² + bx + c

• f(x) = P(x)/Q(x) where P(x) and Q(x) are polynomials

• f(x) = √x

The limit of f(x) as x approaches 'a' is L (lim x→a f(x) = L) if:

• f(a) = L

• For every 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

A one-sided limit, lim x→a⁻ f(x), refers to the limit as x approaches 'a' from which direction?

• The right

• The left

• Both the left and the right

• Neither the left nor the right

The Squeeze Theorem (Sandwich Theorem) states:

• If f(x) ≤ g(x) ≤ h(x) and lim f(x) = lim h(x) = L, then lim g(x) = L.

• If f(x) = g(x) for all x, then lim f(x) = lim g(x).

• If lim f(x) and lim g(x) exist, then lim (f(x) + g(x)) exists.

• If lim f(x) = ∞, then lim 1/f(x) = 0.

A function is continuous at a point 'a' if:

• f(a) is defined, lim x→a f(x) exists, and lim x→a f(x) = f(a).

• f(a) is undefined.

• f(x) is differentiable at x = a.

• lim x→a f(x) = ∞