what is an easy way to find the domain and range of a function?
what is an easy way to find the domain and range of a function?
Domain The domain of a function is the complete set of possible values of the independent variable.
In plain English, this definition means:
The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
When finding the domain, remember:
- The denominator (bottom) of a fraction cannot be zero
- The number under a square root sign must be positive in this section
How to find the domain In general, we determine the domain of each function by looking for those values of the independent variable (usually x) which we are allowed to use. (Usually we have to avoid 0 on the bottom of a fraction, or negative values under the square root sign).
Range The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
In plain English, the definition means:
The range is the resulting y-values we get after substituting all the possible x-values.
How to find the range - The range of a function is the spread of possible y-values (minimum y-value to maximum y-value)
- Substitute different x-values into the expression for y to see what is happening. (Ask yourself: Is y always positive? Always negative? Or maybe not equal to certain values?)
- Make sure you look for minimum and maximum values of y.
- Draw a sketch! In math, it's very true that a picture is worth a thousand words.
The domain of a function is the complete set of possible values of the independent variable.
In plain English, this definition means:
The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
When finding the domain, remember:
- The denominator (bottom) of a fraction cannot be zero
- The number under a square root sign must be positive in this section
How to find the domain
In general, we determine the domain of each function by looking for those values of the independent variable (usually x) which we are allowed to use. (Usually we have to avoid 0 on the bottom of a fraction, or negative values under the square root sign).
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain.
In plain English, the definition means:
The range is the resulting y-values we get after substituting all the possible x-values.
How to find the range- The range of a function is the spread of possible y-values (minimum y-value to maximum y-value)
- Substitute different x-values into the expression for y to see what is happening. (Ask yourself: Is y always positive? Always negative? Or maybe not equal to certain values?)
- Make sure you look for minimum and maximum values of y.
- Draw a sketch! In math, it's very true that a picture is worth a thousand words.
