For f(x) we have:
- domain: set of all real numbers.
- range: set of all real numbers.
And for g(x):
- domain: set of all real numbers
- range: set of all real numbers such that y ≥ 5.
How to get the domain and range of each function?
The domain of a function is the set of inputs that we can use on the function, and the range is the set of outputs.
a) f(x) = -2x
This is just a linear equation, as you can see, for no value of x we have a problem, then the domain is the set of all real numbers.
Similar for the range, it covers the set of all real numbers, then:
- domain: set of all real numbers.
- range: set of all real numbers.
b) g(x) = 0.5*x² + 5
This is a quadratic function, so the domain is the set of all real numbers again.
Now the range will have a minimum, which is at the vertex of the parabola.
For the parabola the vertex is at x = 0:
g(0) = 0.5*0² + 5 = 5
Then the range is the set of all real numbers equal to or larger than 5.
- domain: set of all real numbers
- range: set of all real numbers such that y ≥ 5.
If you want to learn more about domain and range:
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