Math 144 – Test 1
Show all work. Simplify all answers. Circle all answers. Leave all answers exact (reduced
fractions not rounded decimals – unless otherwise indicated).
1) Solve 25 r ! 13 = 25 ! r
2) Graph the line containing the point (-1,2) that has slope m = -2
3) Find the equation of a line that contains the points (1, 3) and (-1,2)
4) For the function f (x) = 2x ! x 2 find and simplify f(1), f(-x), and f(x-h)
5) Find the domain of the function G(x) = 1 ! 2x
6) For f (x) = 3x 2 + 4 and g ( x) = 2 x ! 3 find and simplify: g ! f
" 52 %
7) Evaluate the expression. $ 1 '
$# ! 3 '&
8
2
(x + 2)4 3(x ! 1)2 ! (x ! 1)3 4(x + 2)3
8) Simplify the expression
((x + 2)4 )2
9) For the function f (x) = x
f (x + h) ! f (x)
a) Find and simplify:
(rationalize the numerator)
h
b) EC: plug h=0 into your answer to part a, and simplify.
10) Simplify ln(x 5 ) ! 3ln x
11) Retail prices are obtained by marking up wholesale prices by 10%. If the retail price is $20,
what is the wholesale price?
12) A publisher for a new novel figures fixed costs at $50,000 and variable (marginal) costs at
$2.00 per book. If the book is sold to distributors for $10 each, how much profit will the
publisher make if they sell 10,000 books?
13) The price-demand function for a widget is p = 10 ! 2x (x is number of widgets, p is price in
dollars). What price will maximize revenue?
14) The graphs of f (x) = x and the related (transformed) function g(x) are shown below.
What is the equation for g(x) ?
15) Sketch the graph of f (x) = (x ! 1)(x + 2)2 (x ! 3) showing the correct general shape of the
graph and the location of each intercept.
16) Write the equation of each horizontal and vertical asymptote for each function below:
x ! x2
1 ! x ! x2
2x ! 3
f (x) =
h(x)
=
g(x)
=
3x + 2x 2
2 + 3x
x2 + 8
! 1$
17) Graph f (x) = # &
" 2%
x
18) Graph f (x) = log 2 x
19) A radioactive element decays at a rate of 10% per year. (Just like continuously compounded
interest, except use a negative interest rate.) If I start with 10 grams, how much will I have in 3
years?
20) How many years will it take $100 to grow to $250 if it is invested at 20% compounded
continuously?
21) Solve for x: log 3 (4x ! 5) = 2
22) Write as a single logarithm and simplify (but leave in logarithmic form):
1
ln 5 ! 2 ln 3 + 3ln 2
2
23) Fully simplify each of the following:
a) log(1, 000, 000, 000, 000, 000)
b) eln x
24) Rewrite:
a) log 5 a = d as an exponent.
b) 10 x = y as a logarithm.