Chapter Test
Sign In
When graphing step functions, be careful with the use of open and closed circles.
Graph:
Domain: 0 ≤ x <12
Range: {- 2, - 1, 0, 1}
Let's observe the given step function. f(x)= 1, & if 0 ≤ x < 3 0, & if 3 ≤ x < 6 -1, & if 6 ≤ x < 9 -2, & if 9 ≤ x < 12
To graph this, we draw a horizontal line at y=1 extending from x=0 to x=3. To indicate that x=0 is contained in the solution set, we place a closed circle at that point. To indicate that x=3 is not contained in the solution set, we use an open circle.
Following a similar process, we can graph the other pieces of the function.
Now that we have graphed the function, we can describe its domain and range.
The domain of a function is the set of x-values for which the function is defined. From the graph (and the function rule), we can see that x can equal any value from 0 to 12, but not including 12. 0 ≤ x < 12
The range of a function is the set of y-values for which the function is defined. From the graph (and the function rule), we can see that y can only equal -2, -1, 0, and 1. {- 2, - 1, 0, 1}