Hi, there--
YOUR QUESTION:
Is the function f(x) = x^3+ 5 for all x element of R an onto function?
ANSWER:
This is the mathematical definition of an onto function: A function f from A to B is called ONTO
if for all b in B there is an a in A such that f (a) = b. All elements in B are used. Such functions
are also referred to as surjective.
Let's see if f(x) = x^3 + 5 satisfies this definition. The function f(x) is a cubic function. On the
coordinate plane, Set A is the domain of the function (all the real numbers) and Set B is
the range of the function (also, the real numbers). The graph is a lazy S-curve that increases
left to right from Quadrant III, crosses the y-axis at (0,5) and into Quadrant I. As you progress
along this curve, very possible y-value is used. Thus the function is ONTO.
Here is a nice explanation with diagrams of ONTO and ONE-TO-ONE functions:
http://www.regentsprep.org/regents/math/algtrig/ATP5/OntoFunctions.htm
Hope this helps,
Mrs. Figgy
