Name: _____________________________________________Date:________________________Period:_____
Algebra 2
Review of Sections 7-1 to 7-3
NON CALCULATOR
Exponential function form:
y  ab x
Exponential Parent function:
y  bx
Translated Exponential Function form:
y  ab x  h   k
𝑎 =Stretch or compress factor
Logarithmic function form:
𝑘 =Vertical shift
ℎ =Horizontal shift
y  log b x
Logarithmic parent function:
y  log b x
y  a  log b x  h  k
Translated Logarithmic Function form:
𝑘 =Vertical Shift
ℎ =Horizontal Shift
𝑎 =Stretch or compress factor
Domain: x-values (read graph left to right)
Range: y-values (read graph down/up)
Without graphing, determine whether the function represents a growth or decay.
Recall: Look at the “b” value!

If b is between 0 and 1, it’s a decay.

If b is greater than 1, it’s a growth.
1
1. y  2 
5
x
15
________________ 2. y   
22
x
________________ 3. y  3 ________________
x
Without graphing, determine the y-intercept for each exponential function.
Recall: Plug in 0 for x and solve for y. State your answer as an ordered pair! (0, #)
1
4. y  2 
5
x
x
________________ 5. y 
15
  ________________
22
6. y  3 ________________
x
Describe how the parent function is transformed for each of the following.
7. y  
1 x
4  2 __________________________________________________________________________
3
1
8. y  1.08 
2
9. y  8
 x 7 
 x 3 
 4 _______________________________________________________________________
 3 ___________________________________________________________________________
10. y  2 log 3 x  1 ________________________________________________________________________
11. y  log 5 x  7  2 _______________________________________________________________________
12. y 
2
log 4 x  5 _______________________________________________________________________
5
Fill in the table, graph the function, and then give the domain and range.
13.
1
y 
4
x
x
y
-2
-1
0
1
13.
2
D = __________________________
3
R = __________________________
y  2 
x
x
y
-2
-1
0
1
2
D = __________________________
3
R = __________________________
Graph the Parent function and its transformation on the same coordinate plane. Be sure to name your
functions!
14. y  23  4
x
𝑥
𝑦=
𝑦=
−2
−1
0
1
2
15. What is the equation of the asymptote of the parent function? ________________
16. What is the equation of the asymptote of the transformation? ________________
Recall: Asymptote is the line that the graph approaches, but never touches!
Logarithmic Functions
If b and y are positive numbers and b  1, then
log b x  y
Rewrite each equation in exponential form.
17. log 2 32  5
18. log 5 1  0
19. log 10 10  1
20.
log 1 2  1
2
Rewrite each equation in logarithmic form.
21. 4 3  64
23. 8 1 
1
8
2
22.  
3
3

24. 6 2  36
27
8

by  x
and vice versa
Evaluate each expression.
25. log 3
1
27
26. log 32 2
27. log 7 343
Complete.
28. Common logarithms have a base of ___________.
29. Logarithms without a base are assumed to have a base of ___________.
30. Write “Y” for yes or “N” for no to indicate whether each logarithm is a common logarithm.
a. ______ log 2 4
b. ______ log 64
c. ______ log 10 100
d. ______ log 5 5
Graphing a Logarithm.
1. Rewrite the logarithmic equation in exponential form.
2. Create a table to find points on the graph of the exponential function.
3. Find the inverse of those coordinates.
4. Graph the logarithmic function using those reversed points.
5. *The graphs of the exponential function and logarithmic function are inverses; they are reflected over
the line _________________!
31. What is the graph of y  log 3 x
𝑥
Point
(𝑥, 𝑦)
Inverse
(𝑦, 𝑥)
What is the domain? : ____________________
y-intercept? : _______________________
What is the range? : _____________________
Vertical Asymptote? : ______________________