Chapter 1: Functions from a Calculus Perspective

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the notation for a function?

Back

Functions are typically denoted by letters such as f, g, or h, followed by parentheses containing the input variable, e.g., f(x).

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a graph of a function. If any vertical line intersects the curve more than once, the curve is not a function.

Front

What is the horizontal line test?

Back

The horizontal line test determines if a function has an inverse. If any horizontal line intersects the graph more than once, the function does not have an inverse.

Front

How do you find the critical points of a function?

Back

Critical points occur where the derivative of the function is zero or undefined.

Front

What is a maximum point in a function?

Back

A maximum point is a point where the function value is greater than the values of the function at nearby points.

Front

What is a minimum point in a function?

Back

A minimum point is a point where the function value is less than the values of the function at nearby points.

Front

What is the composition of functions?

Back

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

Front

What is the difference between a function and its inverse?

Back

The inverse of a function reverses the roles of inputs and outputs. If f(x) = y, then f^(-1)(y) = x.