Determine the set of all possible output values (range) for different types of functions.
Function Parameters
Range Analysis
[0, β)
Range
The set of all actual output values (y-values)
Vertex / Extremum(0, 0)
Limit TypeMinimum
About this calculator
What is the Range?
The range of a function is the set of all possible values that the function can produce as output (y-values) when every possible input (x) from the domain is used. While the domain is 'what goes in', the range is 'what comes out'.
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Pro Tips
Linear Functions: Almost all linear functions (except horizontal ones) have a range of all real numbers (-β, β).
Quadratic Functions: The range is always restricted by the vertex. If the parabola opens up (a > 0), the range is [k, β).
Absolute Value: Like quadratics, absolute value functions have a range restricted by their 'tip' or vertex.
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Fun Facts
"The term 'Codomain' is often confused with 'Range'. The codomain is the set of *possible* outputs, while the range is the set of *actual* outputs."
"The range of trigonometric functions like sin(x) and cos(x) is always restricted to [-1, 1]."
"Exponential functions like eΛ£ have a range restricted to (0, β) because they never reach zero or become negative."
Formula: Quadratic f(x) = a(x-h)Β² + k => Range: [k, β) if a > 0
