This is a free lesson from our course in Algebra I
In this lesson you'll learn how to find the range and domain of a function from
its equation. The range of f is the set of all values that the
function takes when x takes values from the domain. Let's take an example
to understand this better. Let's say we have a funtion y = f(x)
= x^{2} + 3. As long as x is a real number, y
is always going to be a real number as well, hence the domain of this function is
x = R. Also, for all values of x, x^{2} is going
to be 0 or higher, hence the range of this function, i.e. the value of f(x) >=
3.
The domain of a function is the complete set of possible values
of the independent variable in the function i.e. the domain of
a function is the set of all possible x values which will make the function
"work" and will output real yvalues.(More text
below video...)
(Continued from above) When finding
the domain, remember:
• the denominator (bottom) of a fraction cannot be zero
• the values under a square root sign must be positive
The range of a function is the complete set of all possible
resulting values of the dependent variable of a function, after we
have substituted the values in the domain i.e. The range of a function
is the possible values of a function that result when we substitute all
the possible yvalues into the function.
When finding the range, remember:
• substitute different xvalues into the expression
for y to see what is happening
• make sure you look for minimum and
maximum values of y
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