FINDING THE DOMAIN AND RANGE OF A FUNCTION

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 $\displaystyle\,g(x) = \frac{\sqrt{x-3}}{x-5}\,$.

SOLUTION:

$x-3\not\lt 0\ \text{ and }\ x-5\ne 0$

$x-3\ge 0 \ \text{ and }\ x-5\ne 0$

$x\ge 3\ \text{ and }\ x\ne 5$

$\text{dom}(g) = [3,5) \cup (5,\infty)$

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 $\,f(x) = |x-5| + 3\,$.

SOLUTION:

Graph $\,f\,$ by starting with $\,y = |x|\,$, shifting it right $\,5\,$ and up $\,3\,$.

$\text{ran}(f) = [3,\infty)$
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

On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.
PROBLEM TYPES:
1 2 3 4 5
AVAILABLE MASTERED IN PROGRESS

(MAX is 5; there are 5 different problem types.)