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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.

Composition of Functions [07/23/1999]

Composition of Functions: Inequalities in the Domain, Inaccuracy in the Book [02/19/2013]
A student wonders why her textbook disagrees with her solution to the domain of a composite function. Doctor Peterson walks through three approaches, as well as a method that checks her answer — and the book's.

Connecting the Dots [02/02/1998]


Constructing Polynomials [01/20/1999]

Continous Random Variables [03/15/2001]
Let c be a constant and consider the density function... find the value of c and the cumulative distribution function F(y); compute F(1); compute P(y greater than .5).



A Continuous Function on a Specified Interval [11/13/2003]
Does there exist a partition of the set X = [0,1) into two subsets A and B and a continuous function f(x) such that x in A ==> f(x) in B and x in B ==> f(x) in A?

Contrapositives and Monotonic Functions [03/17/2003]


Crossing a Canyon [5/10/1995]
Basically, we're trying to cross a canyon. From a point on one side, a rope stretches across and drops ten feet vertically...


Defining Positive Zero [03/07/2003]

Defining Transcendental Functions [02/05/2001]
Can you give me a clear definition of "transcendental function"? How are algebraic, elementary, and transcendental functions related?

Degree of Constant Function [11/08/2001]

Dependent and Independent Variables [05/24/2005]
A look at how functions can be written in different ways, leading to different variables being considered dependent or independent.

Derivative of an Odd Function [02/27/2002]

Derivatives [12/07/1998]

Derive the Function of Celsius to Fahrenheit [09/22/1997]
How do you get the equation of Celsius to Fahrenheit and vice versa? How would you graph that function?

Determining Roots of a Function [04/03/2003]
I know that under specific conditions we can calculate the roots of a function using the Newton-Raphson Method. The Newton-Raphson method uses the tangent to approximate the root. I want to know if there is a method to approximate the root with a parabola instead of the tangent.

Determining whether a Function is Even or Odd [11/09/1999]
How do you determine whether a function is an even function, an odd function, both, or neither?

Differentiating a Quotient [08/29/1997]
Given that g(x) = x-4/x+3, find: {g (x+h) - g(x}/h).

Differentiating Variables from Functions [02/03/2004]


Discrete or Continuous Problem [2/13/1995]
Mae spends $65 a week on food. After 3 weeks she has $415 left in her food budget. What my math class wants to know is: Is this continuous or discrete?

Discussion of Euclidean Functions of Z [06/10/2008]
Can you help me give a description of all Euclidean functions of Z? The common example is of course the absolute value function, but it seems to me that other weird Euclidean functions can be constructed, too.

Does the Order Matter When Transforming a Function? [08/31/2007]
A function such as -2(x - 5)^3 + 3 has a reflection, a vertical stretch, a horizontal shift, and a vertical shift. How do you decide in which order to perform the translations? Does it matter?


Domain and Range [08/25/1997]
Can you please explain about domain and range?

Domain and Range of a Function [03/05/2004]
Given f(x) = 2x, find the domain and range of the function.

Domain and Range of an Inverse Function [03/18/1998]
Why is the domain of a function equal to the range of the inverse function?

Domain and Range of Functions [03/20/2003]

Domain and Range of x^x [08/24/1998]
What is the domain and range of x^x?


Domain of a Composite Function [08/30/2001]
I don't completely understand how to find the domain of a composite function. Could you please explain it?






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