1. Math 025 Section 7.1 Coordinate Systems

2. y-axis
Quadrant II
Quadrant I
x-axis
Origin
Quadrant III
Quadrant IV

3. Each point in the plane can be identified by an ordered pair
(5, 7)
The ordered pair tells the location of the point with reference to the origin
Example: (5, 7)
The numbers in the ordered pair are called the coordinates of the point
5 is the x-coordinate or abscissa
7 is the y-coordinate or ordinate
The graph of a point is a dot placed at the location of the point

4. Graph the following ordered pairs: A(-2, -3) B(3, -2) C(0,2) D(-3,0)y C D x B A

5. Give the coordinates of A and B Give the abscissa of Cy
Give the abscissa of C B
Give the ordinate of D C A D x
Answers:
Coordinates of A are (-4,2)
Coordinates of B are (4, 4)
Abscissa of C is -1
Ordinate of D is 1

6. Objective: To check solutions of an equation in two variables.
Question: Is (-3, 7) a solution of y = -2x + 1 ?
y = -2x + 1
Replace x with -3
7 = -2(-3) + 1
Replace y with 7
7 =
7 = 7
Both sides of the equation simplify to the same thing.
Yes, (-3, 7) is a solution

7. Objective: To check solutions of an equation in two variables.
Question: Is (3, -2) a solution of 3x – 4y = 15 ?
3x – 4y = 15
3(3) – 4(-2) = 15
Replace x with 3
Replace y with -2
9 + 8 = 15
17 = 15
Both sides of the equation are not the same.
No, (3, -2) is not a solution

8. Problem: Graph the ordered-pair solutions of 2x – 3y = 6
Problem: Graph the ordered-pair solutions of 2x – 3y = when x = -3, 0, 3 and 6
Solve 2x – 3y = 6 for y
- 3y = -2x + 6
y = 2x – 2 3 x y 5 -3
2(-3) – 2 -4 3
2(0) – 2 -2 3 -5 3
2(3) – 2 3 6
2(6) – 2 2 3

9. Problem: Graph the ordered-pair solutions of y = 2x – 1
Problem: Graph the ordered-pair solutions of y = 2x – when x = -2, 0, 1 and 3
y = 2x - 1 x y 3 -2 -5 -1 1 1 3 3 5

10. Objective: To determine if a set of ordered pairs is a function
Definition of a relation
A relation is any set of ordered pairs.
Example: {(2, 3), (5, -4), (-7, 8), (-12, 8)}
Definition of a function
A function is a relation in which no two ordered pairs have the same first coordinate.
Example: {(2, 3), (5, -4), (-7, 8), (-12, 8)}
is a function

11. Objective: To determine if a set of ordered pairs is a function
State whether each of the following relations is a function No
{(5, 3), (5, -4), (-7, 12), (-5, 12)}
Yes
{(3, 3), (6, -5), (-7, 12), (-5, 12), (8, 3)}
{(3, 3), (6, 3), (-7, 3), (-5, 3), (8, 3)}
Yes
{(2, 3), (2, -5), (2, 12), (2, 15), (2, 9)} No

12. Does the equation express y as a function of x ?
y = 0.5x where x Î {-4, 0, 2}
x y
The relation for this domain is -1
{(-4,-1), (0, 1), (2, 2)} 1 2
Yes, the equation is a function

13. Does the equation express y as a function of x ?
|y| = x where x Î {-2, 0, 2}
x y
When x = 2, |y| = 0 so y = 0 -2
When x = 0, |y| = 2
so y = 2 or y = -2 2
When x = 2, |y| = 4
so y = 4 or y = - 4 -2 2 4
The relation for this domain is 2 -4
{(-2, 0), (0, 2), (0, -2), (2, 4), (2, -4)}
No, the equation is not a function

14. Objective: To evaluate a function that is written in function notation.
When an equation such as y = x defines y as a function of x, the following function notation is often used to emphasize that the relation is a function
f(x) = x2 + 3
f(x) is read “the value of the function f at x”
or “f of x”
The expression f(4) means “the value of the function when x = 4”
so f(4) = (4)2 + 3 =
= 19
This process is called evaluating the function

15. Objective: To evaluate a function that is written in function notation.
Problem: Given f(x) = 5x find f(2)
Solution:
f(x) = 5x + 1
f(2) = 5(2) + 1
= 11
Problem: Given Q(r) = 4r2 – r – find Q(3)
Solution:
Q(r) = 4r2 – r – 3
Q(3) = 4(3)2 – (3) – 3
= 36 – 3 – 3
= 30