Relations and Functions in Algebra Quiz

A relation is any set of ordered pairs, and (2, 3) represents an ordered pair.

The function f(x) = 2x - 1 has a range of all real numbers.

The expression y = x^2 + 1 represents a function.

The composition (f ∘ g)(x) of the given functions is 4x^2 - 4x + 1.

The domain of f(x) = √(x + 5) is x ≥ -5.

The composition (f ∘ g)(x) for the given functions is 6x^2 + 8x - 5.

The domain of f(x) = 1/(x^2 - 4) is x ≠ ±2.

The composition (f ∘ g)(x) for the given functions is 4x^2 + 4x + 1.

The domain of f(x) = sqrt(x - 3) is x ≥ 3.

The composition (g ∘ f)(x) for the given functions is 8x^3 + 4x + 1.

The domain of f(x) = 1/(x^2 + 4) is all real numbers.

While every function is a relation, not every relation is a function.

A one-to-one function is represented by a graph where every vertical line intersects at most once.

The period of the given function is 2π.

The range of f(x) = e^x is x ≥ 0.

A many-to-one function is represented by a graph where multiple inputs may map to the same output.

The period of the tangent function is 2π.

The range of f(x) = log(x) is all real numbers.

The natural logarithm function h(x) = ln(x) is one-to-one.

The period of the secant function is 2π.

The range of f(x) = e^(-x) is x > 0.

A circle represents a many-to-many relation.

The period of the cosecant function is 2π.

The range of f(x) = log(x + 1) is all real numbers.