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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.

All About Functions [11/06/1996]
Could you please explain functions?

Defining 'Undefined' [09/15/2003]

Definition of the Signum Function [05/31/2000]


Function Machine [10/26/1996]
How do you find the domain and range of a function?

Function Tests [02/19/1997]
What is the reasoning behind the vertical and horizontal line tests?

Interval Notation [4/1/1996]


Rational Inequality [10/09/2001]

Sometimes, Always, or Never True? [02/12/2002]
Is this statement always, sometimes, or never true: f(g(x))=g(f(x)) ?

What Are Quadratic Functions? [02/27/2003]

What is a Function? [06/14/2001]
I've read many definitions and I've asked many teachers, but I still don't completely understand.




2^x = x^2 [02/13/2002]
Find the real value without graphing.

ABS(f(x)) and f(ABS(x)) Graphs [08/27/2013]
A student seeks help graphing functions transformed by absolute values variously acting on the whole function, and on just the argument, by itself. Doctor Peterson talks through sketching and checking such transformations.

Absolute Value and Continuity of Functions [09/15/2004]
I know that the absolute value of a continuous function is also continuous. Is the opposite true? That is, if the absolute value of a function is continuous, is the function continuous?

Algebraically Equivalent Functions [06/27/2002]
If a function can be manipulated so that it can't have a denominator equal to zero (and thus be undefined for that value), why is the original function still considered undefined at that value?


Approximating f(x - 1) in Terms of Its First and Second Derivatives [08/15/2012]
A student seeks help verifying that f(x - 1) = f(x) - f'(x) + (1/2)f''(e). Doctor Schwa renames the function and applies Taylor's expansion to clarify where to substitute, providing just the right boost.

Are All Functions Equations? [07/16/2001]

Assigning Random Numbers [05/16/2000]
I am using a programming language and have a random number generator that can generate a random number of 0, 1, or 2. How can I assign those three values to 4, 12, and 14?

Asymptote of a Function [06/02/2002]

Big O Notation and Polynomials [04/12/2001]

Big O, Omega, and Sigma [09/19/2001]
I cannot understand how something can be both Big O and Omega (aka Big Theta). A general explanation of O/Omega/Theta would be helpful.

Brackets or Parentheses? [01/07/1997]

Calculus of Piecewise Functions [06/07/2003]



Catenary Curve [03/30/1999]
Find the vertex of a catenary curve.

Chaotic Functions [10/30/2000]
Can you give some mathematical examples of chaos theory?

Circular Functions [01/27/2001]
How do you define circular functions? Can you give me an example?

Closed Form Solutions [09/16/1997]
What is the exact mathematical definition of a closed form solution?

Coconuts, Forwards and Backwards [02/02/2010]

Composing Functions [12/02/1998]
I'm trying to find f-of-g where f(x) = 2x and g(x) = 3x^2 + 1. What happens when you compose two functions?

Composite Functions [4/5/1996]

Composite Functions [01/11/1998]
My students can't understand composite functions.

Composite Functions Using Logarithms [3/10/1996]
Suppose f and g are functions defined by f(x) = x+2 and g(x) = x. Find all x > -2 for which: 3^[g(x)*logbase3 f(x)] = f(x).



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