Pre-Calculus Ch 7 Review Sheet
Name __________________________________ Date ___________
1. Solve the following:
a. log 7 (x  1)  log 7 (x  5)  1
d.
5
5

x
4  3e
13
b. 2 cos2 x  cos x  1
c. 3.2  2ln( x  1)  5
e. 92 x  27 x2
f.  3 tan x  4  5
2. Rewrite y  x 2  6 x  7 in standard form y  ( x  h)2  k by completing the square. Identify the vertex.
a. y  x 2  6 x  4
b. y  x 2  10 x  32
3. Complete the square & find the center and radius of the circle.
a. x 2  y2  12x  10y  3
b. x 2  y2  2x  6y  31
c. y  x 2  5x  1
c. x 2  y2  4x  8y  12
4. Simplify the following writing all exponents as positive-rational numbers:
1
a. 7x 2 y
 2 x 4  5 
b. 
3  3 
 xy   y 
5. Divide
x 2  x  29
x6
6. Find the quotient & remainder of
lim f ( x)  ____
x3
x4
lim f ( x)  ____ lim f ( x)  ____
x3
x3
7. Find the quotient & remainder
9. Show whether x  3 is a factor of x5  1x  3x4  3
10. Use the graph to evaluate each of the following:
lim f ( x)  ____ lim f ( x)  ____ lim f ( x)  ____ f (4)  ____
x4
2
( x4  x3  7 x2  6 x  8)  ( x2  2 x  8)
x 1
x2 1
4
8. Show whether x  5 is a factor of x3  4 x2  11x  30 .
x4
 12 f 3 g 6 
c. 

9
 3f

f (3)  ____
lim f ( x)  ____
f ( x) f ( x)
x 0
lim f ( x)  0
x ?
11. Evaluate:
2
lim 4 xx16
x4

2
lim x 
x  4 4 x 16
2
lim x 
x  4 x 16
2
lim f ( x)  ____
Is f(x) continuous or discontinuous? ________________________
2
g (0) 
2
g (1) 
lim x  4
x? 4 x 16
13. Review from Algebra 2: Solve each inequality.
a. x 2  4x  12
b. 6x 2  11x  3
lim g ( x) 
x 
x  
lim x 
x0 4 x 16
x 
lim g ( x) 
x  1
x
lim

x   4 x 16
x  
lim f ( x)  ____
12. Evaluate:
Given the function
x5
g ( x) 
2
x  2x  1
c. x  5  7
lim g ( x) 