Week - In - Review 1: Sections 1.1 - 1.3 (part)
1. Sketch a graph of equation in a rectangular coordinate system:
(a) f ( x)  y  
(b) 5x  6 y  15
(c) y   2
(d) x  3
2
x2
3
2. (a) Find the equation of the line through the points (2, 3) and (- 3, 7). (b) Find the equation of the line
parallel to the line in part (a) and passing through the point (3, 5). (c) Find the equation of the line
perpendicular to the line in part (a) and passing through the point (1, 4).
(a)
(c)
(b)
1
5
3. If cos  , 0 
 

2
, find the other 5 trig functions.
4. Solve the following equations for x,
(a) 2 cos  1  0
0    2 :
(b) tan sec  2 tan
5. Simplify the following expressions completely:
1


2
 4x  2
 6a3/ 4 

(b) 
 15a 1/ 3 


(a) 

4 
y


 (8x) 1/ 3 

(c) 
 12x1/ 4 


2
2
6. Solve the following equations for x:
(a) 2 x 22 x 3 
1
2
(c) x2e x  5xex  0
7. Solve each of the following for x:
(a) logb x 
2
1
logb 8  logb 9  logb 6
3
2
(b) log(x 1)  log(x 1)  1
(b) 53  (x  2)3
8. A certain radioactive isotope decays at a rate such that 85% of the initial amount remains after 4 hours.
(a) Find the decay rate and the general function representing the decay of this particular isotope.
(b) How much of the isotope remains after 40 minutes if the initial amount was 10 mg.
9. How long (in minutes) will it take a certain population of bacteria to triple if its growth rate is 2.5?
10. Review of Basic Graphs
11. Graphs of y  sin ,
y  cos , y  tan
12. Review of Rigid and Non-Rigid Translations.
13. (a) Show f ( x)  y 
x  3  1 is one-to-one.
(b) Find f 1 , its domain and range.
(c) Graph f (x) and f 1 , together with the line y = x.
1
14. Find f given f ( x) 
1
.
x 1