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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.
 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?
 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?
 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?
 Range and Domain of a Graph [02/12/1999]

Determine the domain and range of the graph of "f" that starts at (
2,3), goes down to (0,0), and ends at (3,4).
 Range of a Function [01/05/1997]

Describe the range of the function g(x) = e^(2x).
 Rate of Change Constant? [03/20/2002]

The rate of change of e^x is e^x. Does this mean that the rate of change
is constant? Why are sinx,cosx,... and sinhx,coshx,.... similar?
 Rational Function RangeFinding, with and without Calculus [06/01/2012]

A student seeks an analytic method for determining the range of (x^2)/(x + 1).
Reinforcing that no one technique exists for all such rational functions with polynomial
degree in their numerator greater than that in their denominator, Doctor Peterson
outlines three approaches for the specific problem presented.
 Real and Rational Numbers [02/27/2001]

How can I show that the number of rational numbers between 0 and 1 is the
same as the number of natural numbers (considering the ordering of
fractions: 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5...)?
 Recognizing a Function From a Graph [09/03/2003]

How do you know whether a graph represents a function?
 Recognizing Functions [09/30/2001]

How do I know when there is a function on a graph?
 Relations versus Functions [10/27/1998]

What is the difference between a relation and a function? What about the
domain and range of a function?
 Remainder Theorem and Synthetic Substitution [06/17/2004]

Given P(x) = x^15  2004x^14 + 2004x^13  ...  2004x^2 + 2004x ,
calculate P(2003).
 Reverse Modulus Operator [10/09/2001]

Is there an operator that would return 2 when we we do 6 * 0, * being
this new operator?
 RootFinding [02/09/1998]

Given a polynomial of 3rd degree: X^3 + 5X  2 = 0, show that this
function has EXACTLY one root over the interval [0,1].
 RootMeanSquare [06/15/2003]

How can I visualize the distance between two functions?
 An SAT Question on Functions [08/23/1998]

Let the "tricate" of a number x be defined as onethird of the smallest
multiple of 3 greater then x...
 Sequence of Integers [08/12/2008]

Find all functions f such that for each n in Z+ we have f(n) > 1 and
f(n + 3)f(n + 2) = f(n + 1) + f(n) + 18.
 Shifting Graphs [08/26/2002]

Why is the graph of y=f(xc) just the graph of y=f(x) shifted c units
to the right?
 Simplifying and Working with Imaginary Numbers [04/11/2008]

What is the rule for simplifying an expression like sqrt(50)/sqrt(5)?
Do you get i*sqrt(10) or i*sqrt(10)? Is there a general rule for
simplifying imaginary square roots with regard to handling the i?
 Sketching a Function [07/06/1998]

Can you help me piece a function together so that the following hold? It
is increasing and concave up on (infinity, 1) ...
 Sketching a Graph Given Information about Its Derivatives [07/30/2005]

We've been learning how to analyze a function by using the first and
second derivatives to test if the graph is increasing/decreasing and
concave up/down. But now we have to sketch the graph given some
information about the derivatives and some specific points on the graph.
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