Topic 1: Introduction and Functions and Limits

What is Differential Calculus?

A branch of calculus that studies limits, derivatives, maxima-minima, and time rates.

What is a function?

If a variable y depends upon a variable x so that every value of x corresponds to a value of y, then y is a function of x.

What is the notation used to express a function?

y = f(x)

What does f(a) mean?

The value of f(x) when x = a.

What is an independent variable?

The variable that is assigned values to compute the dependent variable; usually x.

What are the two main kinds of functions?

Algebraic and transcendental functions.

What are examples of algebraic functions?

Rational and irrational functions.

What are examples of transcendental functions?

Trigonometric, inverse trigonometric, exponential, and logarithmic functions.

What is a one-valued function?

A function where every value of x corresponds to only one value of y.

What is a two-valued function?

A function where every value of x corresponds to two values of y.

What are the branches of y² = x? y = sqrt(x) and y = -sqrt(x).