Math 7 A
Summer 2014
NAME _______________________
Show necessary work to receive credit
1. Solve:
(a)
log 1 125  x
(b)
5
83 x2  4
2. Solve each equation for x . Give an exact solution.
(a) log (5 x)  log ( x  1)  4
3. If log b 2  0.36 and
(a)
(b) 5
3 x 5
4
log b 5  0.83 , find the following:
log b 40
(b) log b
2
3
5
5
2
5
2
(a) Graph y  2 x  10 x  11, x 
by finding the vertex. Determine whether it is a one-to-one
2
2
4. Given: y  2 x  10 x  11, x 
function or not. And then find the domain and the range of the given function.
(b) Find the inverse function of
(c) Graph the inverse function f
(d) Show that f ( x) and f
1
f (x )
1
( x) on (a). And then find the domain and the range of f 1 ( x)
( x) are inverse to each other.
5. Solve the inequality. Graph the solution set and write the solution set in interval notation.
p
 3p
p4
6. Melanie wants to invest $10,000 in a CD account. One plan offers 5% compounded quarterly. Another
offers 4.85% compounded continuously.
(a) Which plan will earn more interest in 5 years?
(b) How much more will the better plan earn?
(c) If Melanie chooses the plan with continuous compounding, how long will it take for her $10,000 to
grow to 15,000?
7. Let
f ( x)  3 x 2  6 x  1
(a) Find the vertex by completing the square.
(b) Find the equation of the axis of symmetric.
(c) Find the x -intercept(s).
(d) Find the y -intercept.
(e) Sate the domain.
(f) State the range.
(g) Graph the function. (plot all the points found above).
8. Given: f ( x)  log 1 x  2  1
3
(a) Find the domain of f (x) in interval notation
(b) Graph f (x)
(c) Determine the range and asymptote(s) from the graph
(d) Find f 1  x 
(e) Find the domain and the range of f 1  x  in interval notation
(f) Graph f 1  x 
____________________________________________________________________________________
Math 7 A
Summer 2014
NAME ________________________
Show necessary work to receive credit
1. Solve for x . Give an exact solution.
(7 pts)
32 x1  5
2. Solve for x . Give an exact solution.
(8 pts)
log 2 x  2  log 2 x  1  2
3. Use the Laws of Logarithms to expand the expression:
l o g3
x2
x x2  4
4

(7 pts)

2
4. Given: f x   x  6 x  9  5, x  3
(28 pts)
2
(a) Graph f x   x  6 x  9  5, x  3 by finding the vertex. Determine whether it is a one-to-one
function or not. And then find the domain and the range of the given function.
(b) Find the inverse function of
(c) Graph the inverse function f
(d) Show that f ( x) and f
1
f (x )
1
( x) on (a). And then find the domain and the range of f 1 ( x)
( x) are inverse to each other.
5. Suppose that $12,000 is invested in a savings account paying 5.6% interest per
year.
(18 pts)
(a) Write the formula for the amount in the account after t years if interest is compounded monthly.
(b) Find the amount in the account after 3 years if interest is compounded continuously.
(c) How long will it take for the amount in the account to grow to $20,000 if interest is compounded
semiannually?
6. Solve for
1
n:
27
f ( x)  log 4 x  3  2
32 n7 
(7 pts)
7. Given:
(a) Find the domain of f (x) in interval notation
(b) Graph f (x)
(25 pts)
(c) Determine the range and asymptote(s) from the graph
(d) Find f 1  x 
(e) Find the domain and the range of f 1  x  in interval notation
(f) Graph f 1  x 
____________________________________________________________________________________
Math 7 A
Fall 2013
NAME ________________________
Show necessary work to receive credit
1.
Given the function f ( x)2 x 2  8 x  3 .
a.
b.
c.
2.
a.
Find the vertex.
Does this vertex represent a maximum or minimum?
Find the range, expressed in interval notation.
Given the function f ( x)  2 x 2  4 x  3 .
Express the function in form f ( x)  a( x  h) 2  k .
b. What is the range in interval notation?
3. A cannon ball is shot into the air. Its height (in feet) above the ground as a function of time (in
second) is given by h(t )  16t 2  64t . What is the cannon ball's maximum height?
4.
An area next to a building is enclosed on 3 sides by a fixed length of fencing (see diagram below).
If the total length fencing is 100 meters, what is the maximum enclosed area by the fence?
5.
Find the domain of the composite function f  g with f ( x) 
6.
a. Find the inverse f 1 the function f ( x) 
3
2
and g ( x)  .
x 1
x
x 1
.
x2
b. What is the domain of f (x) ?
c. What is the domain of f 1 ( x) ?
x
7.
1
1
a. Graph the functions f ( x )    and g ( x)   
2
2
x2
1 .
b. Draw any asymptotes (as dashed lines) and indicate the equation of each asymptote.
c. What are the intercepts (coordinates) of each function?
d. What is the range of the function g (x ) ?
8.
a. Graph the function f ( x)  4 x and g ( x)  2  4 x  2 .
b. Draw any asymptotes (as dashed lines) and indicate the equation of each asymptote.
c. What are the intercepts (coordinates) of each function?
d. What is the range of the function g (x ) ?
Solve the equation 92 x  27 x  31
2
1
10. Solve the equation e x  e 3 x  2
e
9.
2
11. If 2 x  3 , then what does 4  x equal?