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Calculus/functions and absolute value

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Expert: - 9/7/2009


Question
Hello there,

How is the graph of y = f(abs(x)) related to the graph of f?

Answer

Absolute Value
Questioner: Maria
Country: United States
Category: Calculus
Private: No
Subject: functions and absolute value
Question: Hello there,

How is the graph of y = f(abs(x)) related to the graph of f?
.............................................................
It's a cousin.  (Well, you asked!)

OK, enough of the bad jokes:

f(|x|) will result in 'f' receiving only positive arguments.

[Argument of  f  is the number  f  'gets'.]

f(- 29) should be the same as  f( + 29), for example.  So if you have already drawn the graph of  f(x), for all x, and you want to make the graph of  f(|x|), do this:

1. Erase the left side, the part for negative x.
2. Put some wet ink on the positive part of the graph.
3. Fold the paper on the y-axis and press it smooth.
4. Unfold and look.

See attached graphs of
y = x^2 - 2x - 3
and
y = (abs(x))^2 - 2(abs(x)) - 3

Paul Klarreich

Expertise

All topics in first-year calculus including infinite series, max-min and related rate problems. Also trigonometry and complex numbers, theory of equations, exponential and logarithmic functions. I can also try (but not guarantee) to answer questions on Analysis -- sequences, limits, continuity.

Experience

I taught all mathematics subjects from elementary algebra to differential equations at a two-year college in New York City for 25 years.

Education/Credentials
(See above.)

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