# Finite Math Examples

Determine if Surjective (Onto)
Function is said to be a surjection or onto if every element in the range is an image of at least one element of the domain. This means the range of must be all real numbers for the function to be surjective. If the range is not all real numbers, it means that there are elements in the range which are not images for any element from the domain.
Range should be all real numbers
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
Multiply each term in by
Multiply each term in by .
Simplify .
Multiply by to get .
Multiply by to get .
Simplify each term.
Multiply by to get .
Move to the left of the expression .
Multiply by to get .
Rewrite as .
The range is the set of all valid values. Use the graph to find the range.
A function is said to be surjective or onto if every element of the range is an image of at least one element from the domain.
Surjective (Onto)

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