Read Domain and Range of a Function from the Algebra I curriculum for a basic introduction to domain and range.
Finding the domain of a function from a formula
The following situations are not allowed, so you must exclude value(s) that cause:
EXAMPLE:
Find the domain of $\displaystyle\,g(x) = \frac{\sqrt{x-3}}{x-5}\,$.
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SOLUTION: $x-3\not\lt 0\ \text{ and }\ x-5\ne 0$ $x-3\ge 0 \ \text{ and }\ x-5\ne 0$ $x\ge 3\ \text{ and }\ x\ne 5$ $\text{dom}(g) = [3,5) \cup (5,\infty)$ |
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Finding the domain of a function from a graph
‘Collapse’ each point into its $x$-value.Finding the range of a function
The range of a function is its output set.It's easiest to find the range when you have the graph of the function!
‘Collapse’ each point into its $y$-value.
EXAMPLE:
Find the range of $\,f(x) = |x-5| + 3\,$.
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SOLUTION: Graph $\,f\,$ by starting with $\,y = |x|\,$, shifting it right $\,5\,$ and up $\,3\,$. $\text{ran}(f) = [3,\infty)$ |
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Master the ideas from this section
by practicing the exercise at the bottom of this page.
When you're done practicing, move on to:
Working with Linear Functions:
finding a new point, given a point and a slope
by practicing the exercise at the bottom of this page.
When you're done practicing, move on to:
Working with Linear Functions:
finding a new point, given a point and a slope