Page 196 - Algebra 1

SOLUTION
Find three ordered pairs for each equation. Check to see which graph includes the ordered pairs.
Equation A: Substituting different values of x into y = x + 3 results in the following ordered pairs: (0, 3), (1, 4) and (2, 5). Only Graph 2 includes these ordered pairs, so Equation A matches Graph 2.
Equation B: For y = ⎪x⎥ + 3, any value for x will have a positive y-value. Equation B matches Graph 3.
Equation C: For y = √x + 3, there cannot be x-values that are negative. Equation C matches Graph 1.
Identifying the Domain and Range
Use the graphs to identify the domain and range of each function.
a.
Example
4
y
8
6
y
=
√x
+
1
4
2
O
x
2
4
6
8
SOLUTION
The domain is x ≥ 0 because you cannot take the square root of a negative number. By inspection of the graph, the range is y ≥ 1.
y
b.
8
f
(x)
=
x
2
-2
4
x
-8
-4
4
8
-4
SOLUTION
-8
By inspection of the graph, the domain is all real numbers and the range is y ≥ -2.
Lesson 30 181