Download W17D1 Log Review and Graphing Warm Up 1

W17D1 Log Review and Graphing
Warm Up
1. Rewrite in logarithmic form my = g
2. Rewrite in exponential form log3 19 = x
3. Find the inverse of f (x) = 2x
1.
logm g = y
x = -2
2.
3x = 19
3. log2 x = f −1 (x)
Lesson 41 Graph Logs
WORKSHEET EDITS - Add line about rewrite in exponential. Before 2. say ”graph the inverse of the function using same
method as pre-question switch x and y. Then just switch the table and rewrite it. 5. change where parentheses are to log4 (x) + 1.
Move 1. from below graphs up to under the y = 2x
Graph the inverse
10
9
8
7
(−2,5) 6
5
4
3
2
1
(1,2)
(2,0)
−1
−5 −4 −3 −2 −1
−2
−3
−4
−5
−6
−7
−8
−9
−10
1
2
3
4
5
Inverse Graph
5
4
3
2
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5
6
7
−2
−3
−4
−5
W1D3 CW Inquiry Graph Worksheet graphing logs
EX 1:
f(x) = 2x
x
y
-1
1
2
0
1
1
2
2
4
3
8
1. f(x) = log2 x –¿ x = 2y
x
y
1
2
-1
1
0
2
1
4
2
8 3
Use a table if needed. The blue one is log2 x and the red one is 2x
5
4
3
2
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5
6
7
−2
−3
−4
−5
Asymptote is x = 0
Domain is x> 0
Range is All Real Numbers
EX 2:
f(x) = log5 (x − 2)
ReWrite method: Write as x = 5y+2
Then do a t-chart by plugging in the y-values and calculating the x-value
x
y
1
25
-2
1
5
-1
1
0
5
1
25
2
x
y
51
25
-2
11
5
-1
3
0
7
1
27 2
Asymptote x = 2
Domain x> 2
Range All Real Numbers
5
4
3
2
1
−5 −4 −3 −2 −1
−1
−2
−3
−4
−5
1
2
3
4
5
6
7
EX 3:
f(x) = log4 (x) + 1
Translation Method
Use the parent function log4 x then shift up 1.
Original Function
5
4
3
2
1
−5 −4 −3 −2 −1
−1
1
2
3
4
5
6
7
1
2
3
4
5
6
7
−2
−3
−4
−5
5
4
3
2
1
−5 −4 −3 −2 −1
−1
−2
−3
−4
−5
Figure 1: Red is log4 (x) + 1
Asymptote x = 0
Domain x> 0
Range All Real Numbers
Rewrite Method: Write as x = 4y−1
x
y
1
16
-1
1
4
0
1
1
4
2
f(x) = −2 log3 (x − 4) + 1
EX 4:
Translation Method
x
y = −2 log3 x
1
0
3
-2
9 -4
1
-1
3
Then shift the points right 4 and up 1
Or Rewrite Method
y = −2 log3 (x − 4) + 1
y − 1 = −2 log3 (x − 4)
y−1
= log3 (x − 4)
−2
y−1
3 −2 = x − 4
y−1
3 −2 + 4 = x
y−1
3 −2 + 4 = x
y
5
1
13
3
7
-1
4.33
-3
2
1
−1
−1
−2
−3
−4
−5
1 2 3 4 5 6 7 8 9 10 11 12 13 14
EX 5:
f(x) = log2 (x − 5) − 3
Write in Exponential Form
(y + 3) = log2 (x − 5)
2y+3 = x − 5
2y+3 + 5 = x
x = 2y+3 + 5
Make a table. But you will make the y = -2, -1, 0 , 1, 2 and then see what x equals.
x
y
6
-3
7
-2
9
-1
13
0
21
1
37 2
Plot the points on the graph
2
1
−4 −2
−1
2 4 6 8 10 12 14 16 18 20 22
−2
−3
−4
−5
Now look back at the equation that we rewrote. It has 5 added at the end. x = 5 is the asymptote.
NOTE: It is the equation x = 5 for log graphs while it was y=4 (for example) for exponentials.
The 3 represents the vertical shift (down) of the graph
The Domain and Range are opposite of exponential graphs.
Domain: x ≥ 5
Range: ARN
Start Monday’s Lesson??
Start CW Simplify Logs Worksheet File Name W2D2 Log Practice half sheet
Answers to W2D2 Log Practice Half Sheet
White Board Problems
2.
log7 (7x + 3) = log7 (5x + 9)
3.
log3 (x2 + x − 6) = log3 14
x=3
x=4
4.
log2 (3x + 11) = 5
5.
log(4x − 8) = 3
x=7
x = 252
6.
log3 (6x + 3) + log2 8 = log2 128
7.
log4 64 − log4 (x − 12) = log2 8
x = 13
x = 13
9.
4 log3 (−9x) = 4
x = −4
x = − 13
x=0
x = 624
8.
10.
12.
2
log5 (x + 3x) = log5 (−8 − 3x)
log3
1
81
+ log9 (x + 1) = −6 + log6 36
log4 3x + 2 log3 9 = log4 256
11.
13.
− 2 log5 (x + 1) = −8
log4 (x2 − 6x) = log4 (10 + 3x)
Exit Pass
1. Expand the expression and simplify log2 4(32) = log2 4 + log2 32 = 2 + 5 = 7
2. Condense the expression and simplify log3 54 − log3 2
log3 27 + log3 2 − log3 2 = 3
1. Find the inverse f(x) = 3x
f −1 (x) = log3 x
2. Solve 8 log1 64 + log3 x = log3 27
x = 31
Solve for x log6 4x = 2
x=
1
3
x = −1, 10