We want to create a table for the rule y=sqrt(x-2) and graph this rule. Let's do these things one at a time.
Making a Table
We are asked to make a table including values ranging from - 1 to 10. Remember that the domain of the square root function excludes the negative values because the square root of a negative number is not a real number.
f(x)=sqrt(x-2)
↙ ↘
cc
Domain & Range
x-2≥ 0 & y≥ 0 [0.4em] ↓ & [0.4em] x≥ 2 &With this in mind, let's construct the table! We can use a calculator to help us find the roots.
x
sqrt(x)
y
- 1
sqrt(- 1-2)=sqrt(- 3)
Not a real number
0
sqrt(0-2)=sqrt(- 2)
Not a real number
1
sqrt(1-2)=sqrt(- 1)
Not a real number
2
sqrt(2-2)=sqrt(0)
0
3
sqrt(3-2)=sqrt(1)
1
4
sqrt(4-2)=sqrt(2)
≈ 1.41
5
sqrt(5-2)=sqrt(3)
≈ 1.73
6
sqrt(6-2)=sqrt(4)
2
7
sqrt(7-2)=sqrt(5)
≈ 2.24
8
sqrt(8-2)=sqrt(6)
≈ 2.45
9
sqrt(9-2)=sqrt(7)
≈ 2.65
10
sqrt(10-2)=sqrt(8)
≈ 2.83
Graphing the Rule
Let's use our table to help us graph the given rule. The first step is to list the ordered pairs (x,y) which represent the rule.
Finally, we can connect those points with a smooth line to create the graph for the given rule. Remember that the domain is all real numbers greater than or equal to 2.
