Which of the twelve basic functions are bounded above?

Question

Ariana Alvarez · Accepted Answer

The Sine function: #f(x) = sin(x)#
The Cosine function: #f(x) =cos(x)#
and
The Logistic function: #f(x) = 1/(1-e^(-x))#
are the only function of the "Basic Twelve Functions" which are bounded above.

Elijah Allen · Answer

undefined The twelve basic functions are typically considered to be:

1. Constant function: $ f(x) = c $
2. Identity function: $ f(x) = x $
3. Squaring function: $ f(x) = x^2 $
4. Cubing function: $ f(x) = x^3 $
5. Square root function: $ f(x) = \sqrt{x} $
6. Cube root function: $ f(x) = \sqrt[3]{x} $
7. Reciprocal function: $ f(x) = \frac{1}{x} $
8. Exponential function: $ f(x) = e^x $
9. Natural logarithm function: $ f(x) = \ln(x) $
10. Sine function: $ f(x) = \sin(x) $
11. Cosine function: $ f(x) = \cos(x) $
12. Tangent function: $ f(x) = \tan(x) $

Among these functions, the bounded above functions are:

1. Constant function: $ f(x) = c $ - Bounded above if $ c $ is finite.
2. Squaring function: $ f(x) = x^2 $ - Not bounded above.
3. Cubing function: $ f(x) = x^3 $ - Not bounded above.
4. Square root function: $ f(x) = \sqrt{x} $ - Bounded above.
5. Cube root function: $ f(x) = \sqrt[3]{x} $ - Bounded above.
6. Reciprocal function: $ f(x) = \frac{1}{x} $ - Not bounded above.
7. Exponential function: $ f(x) = e^x $ - Bounded above.
8. Natural logarithm function: $ f(x) = \ln(x) $ - Not bounded above.
9. Sine function: $ f(x) = \sin(x) $ - Bounded above.
10. Cosine function: $ f(x) = \cos(x) $ - Bounded above.
11. Tangent function: $ f(x) = \tan(x) $ - Not bounded above.

So, the functions bounded above among the twelve basic functions are the constant function, square root function, cube root function, exponential function, and sine function.