Precalculus - Week 4 Flashcard

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

Define the domain of a function.

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (dependent variable) that result from using the function.

Front

Explain the concept of a limit in calculus.

Back

A limit is a value that a function approaches as the input approaches some value. It is fundamental in defining derivatives and integrals.

Front

What is the difference between a continuous and a discontinuous function?

Back

A continuous function has no breaks, jumps, or holes in its graph, while a discontinuous function has at least one point where it is not continuous.

Front

Define a polynomial function.

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the solutions of a quadratic equation ax^2 + bx + c = 0, given by x = (-b ± √(b² - 4ac)) / (2a).

Front

Explain the concept of asymptotes.

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique.

Front

What is the difference between even and odd functions?

Back

An even function satisfies f(-x) = f(x) for all x, while an odd function satisfies f(-x) = -f(x) for all x.

Front

Define the term 'slope' in the context of linear functions.

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).