Download Module 13/15 Review NAME: _______________________________ *Section 1: 13.2/13.3 Graphing Exponential Functions

Module 13/15 Review
NAME: _______________________________
*Section 1: 13.2/13.3 Graphing Exponential Functions
#1 – 3: Identify b, whether growth or decay, identify the Horizontal Asymptote & identify the original equation.
Then identify the Three Reference Points for each Function. Do not graph!
1 𝑥
1
1. 𝑔(𝑥) = (5𝑥+3 ) − 2
3. 𝑔(𝑥) = 2(4𝑥−3 )
2. 𝑔(𝑥) = 3 ( ) + 3
2
6
#4 & 5 Graph and Give the Domain & Range of each function.
1 𝑥−3
1. 𝑔(𝑥) = 2 ( )
3
2. 𝑔(𝑥) = −2(4)𝑥+1 + 3
−1
y
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
Domain: ____________ Range: ______________
Domain: ____________
1
2
3
4
5
x
Range: ______________
*Section 2: 15.1 Logarithms (Intro, Properties, & Exponential Equations)*
Rewrite in Exponential Form
1. log525 = 2
2. Log3 27 = 3
3. log m = n
Rewrite in Logarithmic Form
1. 112 = 121
2. 12 -2 =
1
144
3. 12w = y
Evaluate the expression without a Calculator. (unroll the log first – the y becomes an exponent. Not multiplication)
1
1. log216 = y
2. log2 = y
4. log88 = y
5. log
8
1
10
=y
3. log 1000 = y
6. log71 = y
Identify All Transformations & Vertical Asymptote of Each Logarithmic Function
1. g(x) = 5 log4x – 4
2. g(x) = 12 log5 (x + 8)
3. g(x) = – log (x – 3) + 6
*Section 3: 15.2 Logarithms (Intro, Properties, & Exponential Equations)*
#1 – 4 Expand each logarithm
1. 𝑙𝑜𝑔4 (6k) 2
2. 𝑙𝑜𝑔
5. log 2n + log 5
#5 – 7 Condense each Logarithm.
𝑤 8
2
3. 𝑙𝑜𝑔 ( )
𝑛3
6. log 8 + 3log m + 2log n
4
7. log 9 – 4log k
4. 𝑙𝑜𝑔(39 ∙ 5)
8. 2log25 – log2m
Express each expression as a single logarithm. Then Evaluate without a calculator.
1. log7 19.6 + log7 2.5
2. log2 76.8 – log2 1.2
3. log11 120
4. log7 715
Use Logarithms to Solve each Exponential Equation.
1. 9n – 3 = 24
4. 3(4n) – 2 = 19
2. 16v + 4 = 36
5. 12(2v) + 1 = 37
3. 2n – 4 + 5 = 24
6. 8 –2a – 5 = 35
*Section 4: 15.3 Solving Logarithmic Equations: #1 – 4 Type 1 (logs on both sides) & #5 – 8 Type 2 (one log to unroll)*
1. log (m2 + 3) = log (–8m – 9)
2. log (4x + 3) = log (10x – 21)
2. log n + log 6 = log (4n + 18)
4.
log25 + log2 x = log2100 – log24
4 log3 x + 9 = 17
5. log w – log 12 = 0
6.
7. log2 (5n – 8) – 8 = –7
8. log m + log 20 = 2
*Section 5: 15.4 Natural Log (ln) & Base e*
Identify the transformations and the asymptote of each natural log function.
1.
g(x) = –ln (x + 2)
2.
g(x) = 5ln x – 7
3.
g(x) =
1
3
ln x + 6
Identify the transformations and the asymptote of each exponential function.
4.
g(x) = –ex + 8 + 2
5.
g(x) = 6ex – 3
6.
Solve the exponential function using natural logs.
7. 6e2x
= 24
9. 4ex – 2 + 8 = 24
1
g(x) = 8 ex – 2
8. 3ex – 5 = 10
10. ex + 9 = 21