General Mathematics – Reviewer: Relations & Functions, Rational Functions, Exponential & Logarithmic Functions

Flashcards covering key concepts from the notes on relations and functions, rational functions, and exponential/logarithmic functions, including definitions, tests, and sample problems.

What is a relation?

A set of ordered pairs showing a relationship between two sets.

What is a function?

A special relation where each input x has exactly one output y.

What is the domain?

All possible x-values.

What is the range?

All possible y-values.

What is the Vertical Line Test?

A graph is a function if no vertical line touches it more than once.

What is a One-to-One Function?

Each x maps to a unique y, and each y comes from exactly one x.

How do you find the inverse of a function?

Swap x and y, then solve for y.

Why is the relation { (2,3), (4,5), (2,6) } not a function?

Because x = 2 has two different y-values.

If a graph passes the vertical line test, what does it indicate?

It is a function.

Given the set {(1,2), (2,4), (3,6)}, what is the domain and the range?

Domain: {1,2,3}; Range: {2,4,6}.

What is the inverse of f(x) = 2x + 1?

f^{-1}(x) = (x − 1)/2.

What is a rational function?

A fraction where the numerator and denominator are polynomials.

What is a domain restriction for rational functions?

Denominator cannot be zero.

What is a vertical asymptote?

The x-value(s) where the denominator equals zero (after simplification).

What does LCD stand for?

Least Common Denominator used to add/subtract rational expressions.

For f(x) = 1/(x−3), what is its domain and vertical asymptote?

Domain: x ≠ 3; Vertical asymptote: x = 3.

Solve the equation x/(x−2) = 3; what is the solution and its domain check in the notes?

x = 3; Domain check in notes says x ≠ 3, so the answer is considered valid.

What is the logarithmic form of a^b = c?

log_a c = b.

What is the base of the common logarithm and its symbol?

Base 10, denoted log.

What is the base of the natural logarithm and its symbol?

Base e, denoted ln.

Which logarithm laws are noted in the notes?

Product, Quotient, and Power laws.

What are the general definitions of domain and range in graphs?

Domain: set of all x-values with corresponding points on the graph; Range: set of all y-values.