1. Warm Up #6 Evaluate each expression for the given value of x.
1. x2 + 5x; x = –2
2. 4x – 3x3; x = 2 –6
ANSWER
ANSWER
–16

5. EXAMPLE 1
Represent relations
Consider the relation given by the ordered pair (–2, –3), (–1, 1), (1, 3), (2, –2), and (3, 1).
a. Identify the domain and range.
SOLUTION
The domain consists of all the x-coordinates: –2, –1, 1, 2, and The range consists of all the y-coordinates: –3, –2, 1, and 3.

6. EXAMPLE 1
Represent relations
Represent the relation using a graph and a mapping diagram. b.
(–2, –3), (–1, 1), (1, 3), (2, –2), and (3, 1).
SOLUTION
b. Graph
Mapping Diagram

7. EXAMPLE 2
Identify functions
Tell whether the relation is a function. Explain. a.
SOLUTION
The relation is a function because each input is mapped onto exactly one output.

8. EXAMPLE 2
Identify functions
Tell whether the relation is a function. Explain. b.
SOLUTION
The relation is not a function because the input 1 is mapped onto both – 1 and 2.

9. GUIDED PRACTICE
for Examples 1 and 2
1. Consider the relation given by the ordered pairs (–4, 3), (–2, 1), (0, 3), (1, –2), and (–2, –4)
a. Identify the domain and range.
SOLUTION
The domain consists of all the x-coordinates: –4, –2, 0 and 1, The range consists of all the y-coordinates: 3, 1, –2 and –4

10. GUIDED PRACTICE
for Examples 1 and 2
b. Represent the relation using a table and a mapping diagram.
Consider the relation given by the ordered pair (–4, 3), (–2, 1), (0, 3), (1, –2), and (-2, -4).
SOLUTION

11. GUIDED PRACTICE
for Examples 1 and 2
2. Tell whether the relation is a function. Explain.
ANSWER
Yes; each input has exactly one output.

13. EXAMPLE 2
Standardized Test Practice
SOLUTION
Let (x1, y1) = (–1, 3) and (x2, y2) = (2, –1).
m =
y2 – y1
x2 – x1 =
– 1 – 3
2 – (–1) = 4 3
ANSWER
The correct answer is A.

14. GUIDED PRACTICE
for Examples 1 and 2
(7, 3), (– 1, 7)
SOLUTION
Let (x1, y1) = (7, 3) and (x2, y2) = (– 1, 7).
m =
y2 – y1
x2 – x1 =
7 – 3
– 1 – 7 = 1 2 –
ANSWER 1 2 –

15. Classify lines using slope
EXAMPLE 3
Classify lines using slope
Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. a.
(– 5, 1), (3, 1) b.
(– 6, 0), (2, –4) c.
(–1, 3), (5, 8) d.
(4, 6), (4, –1)
SOLUTION
1 – 1
3– (–5) =
m = a. 8
= 0
Because m = 0, the line is
horizontal.
– 4 – 0
2– (–6) =
m = b.
– 4 8 = 1 2 –
Because m < 0, the line falls.

16. Classify lines using slope
EXAMPLE 3
Classify lines using slope
Without graphing, tell whether the line through the given points rises, falls, is horizontal, or is vertical. a.
(– 5, 1), (3, 1) b.
(– 6, 0), (2, –4) c.
(–1, 3), (5, 8) d.
(4, 6), (4, –1)
SOLUTION
1 – 1
3– (–5) =
m = a. 8
= 0
Because m = 0, the line is
horizontal.
– 4 – 0
2– (–6) =
m = b.
– 4 8 = 1 2 –
Because m < 0, the line falls.

17. a. b. EXAMPLE 4 Classify parallel and perpendicular lines
Tell whether the lines are parallel, perpendicular, or
neither.
Line 1: through (– 2, 2) and (0, – 1) a.
Line 2: through (– 4, – 1) and (2, 3)
Line 1: through (1, 2) and (4, – 3) b.
Line 2: through (– 4, 3) and (– 1, – 2)
SOLUTION
Find the slopes of the two lines. a.
m1 =
–1 – 2
0 – (– 2) =
– 3 2 3 2 –

18. EXAMPLE 4
Classify parallel and perpendicular lines
m2 =
3 – (– 1)
2 – (– 4) = 4 6 2 3
ANSWER
Because m1m2 = – 2 3
= – 1, m1 and m2
are negative reciprocals of each other. So, the lines are perpendicular.

19. EXAMPLE 4
Classify parallel and perpendicular lines
Find the slopes of the two lines. b.
m1 =
–3 – 2
4 – 1 =
– 5 3 = 5 3 –
m2 =
– 2 – 3
– 1 – (– 4) =
– 5 3 = 5 3 –
ANSWER
Because m1 = m2 (and the lines are different), you can conclude that the lines are parallel.

20. Classwork Assignment
WS 2-1 (1-11, all)
WS 2-2 (1-21 odd)