Write bxponential and Linear Equations
To Write Linear Equations:
-Find slope between t w o points.
-Use point-slope form and/or slope-intercept form.
Ex 1: Write a linear function whose graph passesthrough
(1, 6) and [2.18].
4
^ ( that i^^^rpendicula^to
E x 2 ; Write the equation of ai lline
Write Exponential Eq. in the Forniy=afo^-^
1. Substitute the x- and y- coordinate of each point into
the equation y = ah"" to obtain t w o different equations.
2. Solve the system.
Ex 4: W r i t e an exponential function y = ab"^ whose graph
passes through (1, 6) and (2,18).
id - A
Ex 5: Write alT^xponential function
passes through the given points.
a) (2, 8), (5,512]
id:""-A
'^^^^^and contains ( 1 5 , ^ )
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_ _5:/
Ex 3: Vyrite the equation for the function graphed below.
10r
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-10;-8 -6 ;
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- 2 4 6 8 10
l/i
I
1
l b " -
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b]
- 5 0 ] , C4i-1250]
(
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c] C3;i086j;C5,38880]
2J
ft)
Ex 6: Write the equation for the function graphed below.
Ex 7: Write the equation for the exponential function
graphed below:
2
-2
0
3
X
-1
1
2
32
8
4
1
16
y
'//7//j
Writing Equations
Name
lfl%it@ a n @quatioti_oftli@^^llri# t h a t p a s s e s through t h e g i v e n points.
1. (2,-4K(7,Q
2 . (-3, 5),
4. (7,-2),(-1,-5)
5 . (4,%(-7,^
-2)
3 . .^.(3^),^,-9);::,
6 , (1, 1),(-11,2)
0
+4
l ^ l C C l i i e g i i ^ i o n o f t h e l i n e t h a t p a s s e s t h r o u g h t h e g i v e n p o i n t a n d Is
p e r p e n d l e u i g ^ o the given line.
7. (2,-3Xi;=l3k + 2
"3
8.
(-l,-3),j=f&+1
S
^ +3 ^ ^( x
M-lte a n equation o f t h e line that p a s s e s through t h e given poiWTliid Is
| i a m i ^ to t h e given line.
1 3 . (-2,0),j^=|
14. (-6,-2),)/=-fcr +
3
l X J I
Write a n equation of the line.
21.
20.
T
'—
!
• J
22.
y
2;4)\
•f
X
—
\,-2)
1
u
14.1)
.... 1
1
X
i
X
'{-2,
i
(4
-1)
Write the equation of the exponential that conl
ns the following two points.
23. {2,18) and (4,162)
24. (2, 20) and (3,40)
25. (4,486) andl6r4374)
26. (1,6) and a
27. (4,256) and (6,4096)
28. (2, 547and (3,162)
5 4 , ^ ; ^ ,
Write the equation of the exponential that models the table
29.
X
Y
31.
-2
1
9
-1 0 1 2
1
1 3 9
3
1
2
-1 0
Y 160 80 40 20 10
X
-2
30.
X
2
X
Y
14^-
5
9^
fb
2
3
14 98 686 J 4802
Y
32.
3
-2
-1 0
1.25 2.5 5
Write the equation of the exponential that matches the graph
1
2
10 20
Review for Exponentials Test
X.
Name:
Determine the average rate of change of f{x) = x^on the interval [2, 6]
i
2. Determine the average rate of change of the function ^efc^^s^or the interval [-1,1].
...•It
41-
'X
-8-10 -
Write the equation of the line that goes through the points (2, 6) and (3,10).
4. Write the equation of the line that goes through the points (9,11) and (2,11).
1(
5. Write the equation of the line that is parallel to the line y = ^ - 7 goes through the point (-3,12).
6. Which exponential function contains the points (1, 2) and (2, 8). DvOT b^+V points
a) y = 4'
b ) y = 2^
c) y = 2(2r
7. Which exponential function contains the point (3,32)?
3/„\
l,^.._4/„\
b) y = | ( 2 r
^
(9'''
c) y =
3
8. G i v e n / M = 2',
find/(5).
(Kto
"fi^
d)y = i ( 4 r
»u:f eacA_ m Calculectcif
i
^
1--uividt b
True,
9. Write the equation of an exponential function that models the following situations:
a. (2,12) and (4,48)
c.
X -1
Y 2
0
6
1
18
b. (5, 8) and (7, 32)
2
54
3
162
X
Y
1 2
-2 -6
3
-54
4
-162
5
-486
10. Graph the following equations
;^ + 5 = - ( x - 4 )
10
-10 -8 -6 .4 -2
-2
. 2 4 8 8 ^
S
8
•10
y =
¥
-2*y
2
60
ss
so
5 -4 -3
-1 C
..4
1 2
3
4 $
4S
40
35
30
-8
as
-to
20
'1$
-18
IS
• 1C
5
?
4
6
8
10