Create a function with a domain of all real numbers and the range all real numbers that are greater than or equal to zero. Provide the function both graphically and in function notation.
f(x) = x² <-- that is, assuming you choose the domain to be all real numbers (if we allow complex numbers then the range has to change--and won't fit)
In fact any even number will work, i.e. f(x) = x⁴, f(x) = x⁶, f(x) = x⁸, etc.
If you want a more exotic function, you can use the fact that an odd function will NEVER provide what you need and thus only look at even functions such that for positive x values provide positive values.
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f(x) = x² <-- that is, assuming you choose the domain to be all real numbers (if we allow complex numbers then the range has to change--and won't fit)
In fact any even number will work, i.e. f(x) = x⁴, f(x) = x⁶, f(x) = x⁸, etc.
If you want a more exotic function, you can use the fact that an odd function will NEVER provide what you need and thus only look at even functions such that for positive x values provide positive values.
Simplest: f(x) = |x|
More complicated:
f(x) = x²(sin(x) + 1), https://www.google.com/search?source=hp&ei=YWgzWra...