Download 9-8 Transforming Formulas

Graphs can help you see patterns in data.
Steps to draw a graph:
1) Choose the scales and the intervals.
2) Draw the graph and plot the data. Estimate
data points that fall between intervals.
10.About $7
11.About $8
12. About 81 hours
 sequence – set of numbers that follow pattern
 arithmetic sequence – find each term by adding
a fixed number (common difference)
Example: 3, 5, 7, 9, …
 geometric sequence – find each term by
multiplying previous term by fixed number
(common ratio)
Example: 3, 9, 27, 81, ……
The sequence is not arithmetic or geometric if
there is no common difference or common ratio.
Conjecture – prediction that suggests what you
expect to happen
Example: 3, 5, 8, 12, 17, …….
6. Start with -8 and add 7 repeatedly; 20, 27, 34
7. Start with 25 and add -4 repeatedly; 9, 5, 1
8. Start with 1 and multiply by 2 repeatedly; 16, 32, 64
9. Start with 2 and multiply by -3 repeatedly; 162, -486,
1458
10. Start with 600 and multiply by -½ repeatedly; -75,
37.5, -18.75
11. Start with ½ and multiply by ½ repeatedly; 1/32,
1/64, 1/128
12. Start with -2 and multiply by -2 repeatedly; -32, 64, 128
13. Start with ¼ and multiply by 1/3 repeatedly; 1/324,
1/972, 1/2916
14. Neither
15. Neither
16. Geometric
17. Both
18. Geometric
19. arithmetic
You can use a table to represent a pattern. Often
you can make a table as your first step in solving a
problem.
Given a rule, you can find the value of a term using
the position.
Let n = the term number.
7. 4,5,6,7
8. 2, 6, 10, 14
9. 5, 10, 15, 20
10. 7, 13, 19, 25
11. ¼, ½, ¾, 1
12. -2, 1, 6, 13
24, 28
4
4n
Multiply each term by 4
24, 28
13. 11n; 110
14. N – 20; -10
15. n/2; 5
16. -3n; -30
17. -18n; 180
18. 100n; 1000
Function – a relationship that assigns exactly one
output value for each input value
Distance you travel in
car depends on time
you drive.
 X is the input
 Y is the output
output = 2 * input
output = 45 * input
y=x+4
y = 3x + 5
y = -9x + 1
y = -8x
y=x+4
y = 3x + 5
y = -9x + 1
y = -8x
0
10
20
30
-4
-3
-2
-1
-1
2
5
8
60 mph
yes
d = 60t
Input
1
2
3
4
5
6
Output
60
120
180
240
300
360
x
1
2
3
4
5
y
-1/2
-1
-3/2
-2
-5/2
x
1
2
3
4
5
Y
2
0
-2
-4
-6
10. C
11. A
12. B
You can use a graph to show the relationship of
how one quantity changes compared to
another .
formula – a rule that shows the relationship between
two or more quantities
Solve each equation for the variable in red.
formula – a rule that shows the relationship between
two or more quantities
Solve each equation for the variable in red.
y = x/z
u = 2t - v
r=p+5
3
Solve each equation for the variable in red.
Solve each equation for the variable in red.
s =p/4
p = qr
s=p+c
Solve each equation for the variable in red.
h = 2A/b
k = hj
t = I/pr