5B.5 - Logs and Exponents Review
Name: ______________________________
Find the Domain, Range, and Asymptote of each function
f  x   log  x  3   2
f  x   3x2  7
3
1.
Domain:________________________
2.
Domain:________________________
Range:_________________________
Range:_________________________
Asymptote:_____________________
Asymptote:_____________________
4. g  x   2x2  3
f  x   ln  x   5
3.
Domain:________________________
Domain:________________________
Range:_________________________
Range:_________________________
Asymptote:_____________________
Asymptote:_____________________
Describe the Transformation in each function
5. f  x   log4  x  1  2
6. f  x   2 x  1
7. h x   3 x1  2
8. f  x   ln   x  1  4
State whether the function is increasing or decreasing
9.
f  x   2x  5
11.
f  x   log3  x  2   7
 1
10. f  x    
2
x 1
2
12. f  x    log4  x   2
5B.5 - Logs and Exponents Review
13. Which has a larger y-intercept?
X
-1
0
1
2
3
4
F(x)
3.5
4
5
7
11
19
Name: ______________________________
14. A) Is the table below an exponential
function or a logarithmic function?
B) Does the function have a vertical or
horizontal asymptote?
C) What is the equation for the
asymptote?
X
F(x)
1.5
-0.631
2
0
4
1
10
2
15. What is the equation of the function
graphed below?
16. What is the equation of the function
graphed below?
17. A) Is the table below an exponential
function or a logarithmic function?
18. What is the Domain and Range for the
graph below?
B) Does the function have a vertical or
horizontal asymptote?
C) What is the equation of the asymptote?
X
F(x)
-2
2.33333
-1
3
0
5
1
11
2
29
3
83
5B.5 - Logs and Exponents Review
Graph the Functions Below
x
19. y  5  3
Name: ______________________________
20.
y  log5  x   1
Transformations_____________________
Transformations_____________________
State 3 points on Graph______________________
State 3 points on Graph______________________
Domain____________ Range______________
Domain____________ Range______________
Asymptote_________________
Asymptote_________________
X-intercept __________ Y-intercept ____________
X-intercept __________ Y-intercept ____________
Increasing or Decreasing
Increasing or Decreasing
x  ______ , f  x   ______
End Behavior:
x  ______ , f  x   ______
x  ______ , f  x   ______
End Behavior:
x  ______ , f  x   ______
22. y   log2  x  1
x 3
21. y  2  1
Transformations_____________________
Transformations_____________________
State 3 points on Graph______________________
State 3 points on Graph______________________
Domain____________ Range______________
Domain____________ Range______________
Asymptote_________________
Asymptote_________________
X-intercept __________ Y-intercept ____________
X-intercept __________ Y-intercept ____________
Increasing or Decreasing
Increasing or Decreasing
x  ______ , f  x   ______
x  ______ , f  x   ______
End Behavior:
x  ______ , f  x   ______
End Behavior:
x  ______ , f  x   ______
5B.5 - Logs and Exponents Review
Name: ______________________________
Find the Inverses of the Functions Below
23.
f ( x)  2 x  1
25. y  log 2 ( x  1)
27.
24.
g ( x)  2 x  3
26.
y  3x 1
28.
29. Are the functions INVERSES of each other? (Show your work in this space)
f ( x)  3 x  2
g ( x) 
x2
3
30. Are the functions INVERSES of each other? (Show your work in this space)
f ( x)  3x 1
g ( x)  log3 ( x)  2