Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math

High School Archive


This page:
  functions checkmark

  Dr. Math

See also the
Internet Library:


About Math

   basic algebra
   linear algebra
   linear equations

Complex Numbers

Discrete Math

Fibonacci Sequence/
  Golden Ratio

     conic sections/
     coordinate plane
   practical geometry

Negative Numbers

Number Theory

Square/Cube Roots


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.



Equivalent Fractions, Exponential Implications [02/17/2011]

Evaluating Composite Functions [1/31/1996]

Everyday Applications of Inverse Functions [11/06/2011]
A student seeks real-world applications of inverse functions. Doctor Peterson starts with an overview before suggesting several examples.


Explaining Independent and Dependent Variables [10/25/2002]
Can you elaborate on the definitions of independent and dependent variables?

Explicit Inverses [04/21/1999]
How do you solve x^x = 5 without graphing or guessing?

Exponentially Varying Functions [11/11/2001]
I'm imagining a function that doubles after a certain interval, then doubles again in half that time, doubles again in a quarter of the original interval, etc. Are there functions that behave this way?

Express a Function in Terms of Another Function [09/18/1997]
The altitude perpendicular to the hypotenuse of a right triangle is 12 cm. Express the length of the hypotenuse in terms of the perimeter.

Fazed by Fourier Transform Phases [11/14/2011]
Complex output from an inverse discrete Fourier transform (DFT) raises doubts: would discarding imaginary values mean losing important information? Doctor Douglas explains why the phase of each Fourier component matters.

Find a Function, Integrals [12/17/1997]

Finding a Formula to Fit Data Points [06/23/2004]
How can I find a formula that contains the points (500,150), (1000,200), and (1500,225) and has the y-value level off as the x-value gets larger?

Finding a Limit by Iterating a Function [04/21/2004]
Given f(x) = 2x/(x + 1), determine the limit as n approaches infinity of f^n(x) for x > 0.

Finding an Inverse Function [8/28/1996]


Finding The Domain and Range of a Function [01/27/2001]
How do I find the domain and range of a function? My problem is f(x) = x squared -2.

Finding the Domain of a Function [09/16/1997]
How do you find the domain of this function: f(x) = (4+x)/(x^2-9) ?

Finding the Domain of a Function [02/10/2009]
I'm having trouble finding the domain of a function. What is the domain and how does it work?


Finding the Function [12/17/1996]
Given five related functions which have only one variable each, find the function that contains same all five variables.

Finding the Inverse of y = x^x [08/31/2006]
I have been trying to find the inverse function for y = x^x and once I exchange x and y I can't find a way to solve for y. Can you help?


Finding x for e^x = cos(x) [06/25/1999]
How can I solve e^x = cos(x) for x?

Find the Function (fog)(x) [07/02/2003]
Let f(x) = 2x-1 and g(x) = (x+5)/2.

Fixed-Point Theorem [05/02/2002]

Floor and Mod Functions Discontinuous [10/10/2001]


Fourier Transforms [10/19/2001]

Fractional Bases in Exponential and Logarithmic Functions [04/06/2009]
In the equation log_a(x) = a^x, can the base be a fraction? Doctor Ali introduces a student to the Newton-Raphson Method and LambertW function.

Functional Equation [02/18/2008]

Functional Transformations Explained and Undone [09/09/2013]
A student wonders why horizontal transformations behave "opposite" to their original functions. Doctor Peterson explains with one example shifted by addition, and another scaled by multiplication.

Function Crossing X-Axis [07/11/2003]
Find the condition that must be satisfied by k in order so that the expression 2x^2 + 6x + 1 + k(x^2 + 2) may be positive for all real values of x.

Function Deduction from Composition [11/19/2013]
Given one function and the result of its composition with a second function, a student wonders how to recover the second function. Doctor Peterson shows how substitution solves such problems; Doctor Rick follows up with a method that relies on the inverse function.

Function Exponentiation Convention [04/21/2013]


Function Its Own Inverse [01/02/1998]
Show that f(x) = X/X-1 is its own inverse.

Functions [11/12/1994]

Functions and Equations [02/10/2001]

Functions and Function Tables [05/11/1999]
I don't understand functions and function tables. Can you help me?


Search the Dr. Math Library:

Search: entire archive just High School Functions

Find items containing (put spaces between keywords):
Click only once for faster results:


parts of words whole words

[Privacy Policy] [Terms of Use]


© 1994-2015 Drexel University. All rights reserved.