TOPICS
This page:
functions
Search
Dr. Math
See also the
Internet Library:
functions
HIGH SCHOOL
About Math
Analysis
Algebra
basic algebra
equations/graphs/
translations
linear algebra
linear equations
polynomials
Calculus
Complex Numbers
Calculators/
Computers
Definitions
Discrete Math
permutations/
combinations
Exponents
Logarithms
Fibonacci Sequence/
Golden Ratio
Fractals
Functions
Geometry
Euclidean/plane
conic sections/
circles
constructions
coordinate plane
triangles/polygons
higherdimensional
polyhedra
nonEuclidean
practical geometry
symmetry/tessellations
History/Biography
Interest
Logic
Negative Numbers
Number Theory
Physics/Chemistry
Probability
Projects
Puzzles
Sequences/Series
Sets
Square/Cube Roots
Statistics
Transcendental
Numbers
Trigonometry

Browse High School Functions
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Composition of functions.
Domain and range.
Inverse of a function.
Piecewise functions.
 Measurable Functions [09/13/2004]

Can you provide some motivation for the definition of a measurable
function?
 Meromorphic Functions [09/18/1998]

What is a meromorphic function?
 The Meteorologists' Theorem [1/6/1995]

Prove the "Meteorologists' Theorem": At any given moment, there are two
diametrically opposite points on the (spherical?) Earth's surface where
the temperatures are equal and the barometric pressure are equal.
 Multiplying Square Roots of Negative Numbers [11/25/2003]

It seems to me there are two possible ways to interpret a problem like
sqrt(2) * sqrt(2). One way I get 2 and the other way I get 2.
Which solution is correct? What's wrong with the other one?
 Mystery Operation: What Do These Strange Symbols Mean? [03/09/2010]

How do you evaluate the composition of two functions when you don't
even recognize their operational symbols? Doctor Ian unravels the
mystery behind weird symbols, explains their instructional purpose, and
uses grouping parentheses to show how to compose functions according to
the order of operations.
 Naming and Graphing Functions [06/16/1997]

Can you tell me about the different families of functions?
 Natural Domain of a Function [03/12/1999]

Some inputs don't make sense for some functions.
 NewtonRaphson Method [02/28/2000]

How can I find the 1st, 2nd, 3rd iterations and the parameters of x^3 
13.1x^2 + 48.48x  46.62 using the NewtonRaphson method?
 NewtonRaphson Method [06/24/2009]

Are there any equations that cannot be solved using the NewtonRaphson
method, regardless of the initial estimate?
 Newton's Method for Finding Roots of Functions [06/03/2003]

Is there an easy way to learn and understand this method or an example
that would allow me to understand the steps taken to work through the
problem?
 Nondifferentiable Functions [11/6/1994]

In my calculus book, it mentions a function that is not differentiable
at any point due to the fact that it is not smooth at any point. It does
not go any farther, and I was interested in hearing more.
 Normalizing Ranges of Numbers [04/22/2002]

How do I convert ranges like 5200 to a scale of 110?
 O and o Functions [01/08/1999]

How do big O notation and little o notation show the relation between two
functions?
 Odd and Even Function Constructions [06/08/1998]

If f is an odd function and g is an even function, how do we combine the
two in various constructions (adding, multiplying, etc.)?
 Odd And Even Functions [01/11/1998]

The differences between odd and even functions, and examples of each.
 One to One Correspondence Between Sets [04/04/1997]

What is the onetoone correspondence between the set of natural numbers
and the set "S" = {1/3, 1/6, 1/12, 1/24, 1/48, ...}?
 Onetoone Function [02/05/1998]

If A = (0,1) and B = (a,b) show that there is a onetoone function from
A onto B.
 ONTO and INTO [07/27/2001]

What is the difference between ONTO and INTO when you describe a
function?
 Onto (Surjective) Functions [11/03/1998]

I don't understand onto functions. Would you please explain them in
detail?
 Order of Transformations of a Function [11/30/2005]

In what order would I perform transformations such as f(x), f(x),
af(x), f(ax), f(x)+a, and f(x+a) if two or more are applied to f(x)?
If I had f(ax+b), would I do the translation or the stretch first?
 Order of Transformations of a Function, Redux [01/31/2017]

A teen gets confused when the graph of a transformation appears to
disproportionately shrink its horizontal shift. Revisiting his example, Doctor
Peterson points out how the transformation shrunk even the shift.
 Order of Transformations of a Function, Yet Again [03/28/2017]

Another teen notices curious translations at play when adding terms to absolute value functions. Doctor Peterson peels back the steps in order to reveal what's really at play — and how the effect holds for all combinations of horizontal transformations.
 Parameter vs. Constant [12/08/2002]

Can you explain the difference between parameter and constant?
 Parameter vs. Temperature Formula [10/28/2002]

I am trying to figure out a formula for frequency vs. temperature.
 The Phi Function [11/21/1998]

What are the conditions on n,m so that phi(n*m) = phi(n)*phi(m)? What is
phi(p^n*q^m)?
 Piecewise Function [10/23/2001]

How do you graph the piecewise function?
 Piecewise Functions on TI Graphing Calculators [02/08/2005]

I was wondering if you could tell me how to graph a piecewise function
on a TI83 plus graphing calculator?
 Piecewise Functions on TI Graphing Calculators, Redux [09/07/2017]

An adult explores how his graphing calculator interprets piecewise functions. With
multiple examples and revealing experiments, Doctor Peterson guides him to the
TI84's Boolean logic, binary multiplication, and beyond.
 Polar Coordinates and Logarithmic Spirals [04/25/2004]

The polar coordinate graph of a logarithmic spiral suggests that for a
given angle, there is more than one possible rvalue, since the graph
continues to spiral around itself. How is it possible for an
angle to be associated with more than one r?
 Possible Values of f(0) [04/19/2002]

If f(x+y) = f(x)f(y), what is (are) the possible value(s) of f(0)?
 Product Notation [10/26/2000]

Can the pi symbol also be used to mean multiplying all the terms in a
series together?
 A Project on Cycloids [01/16/1999]

Can you explain cycloids? How do you work with the parametric equations?
What are their properties? How are they related to time?
 Proving One Function is Greater Than Another [11/1/1996]

Prove that if n is a positive integer and x > 0, then x^n + 1/(x^n) >
x^(n1) + 1/[x^(n1)].
 Proving Subsets [07/01/2003]

Given the function f:X > Y and subsets A of X and B of Y, prove
the following statements: A is a subset of f^{1}(f(A)); f(f^{1}(B))
is a subset of B.
 PSAT Math Question on Functions [10/17/2003]

For all values of r, let *r be defined as *r = (r + 2)/2. If *4
= x, then *x = ?
 Purpose of Absolute Value and Piecewise Functions [12/09/2001]

What is the purpose of absolute value functions and of piecewise
functions?
 Quarter Circles [12/20/1996]

Find a function that graphs a quarter of a circle in quadrants II and IV.
 Raised Cosines [01/28/2001]

What are raised cosines, and how do they work?
 Range [04/02/2002]

If f(x) = x3/x+3, I know the domain to be all Reals except for 3. The
range, however, is all Reals except for 1. I don't know how they get the
1 algebraically.
 Range and Codomain of a Relation [03/27/2004]

What is the difference between the range and the codomian of a relation?
Page: [<prev]
1
2
3
4
5
6
7
8
[next>]
