Exam 1 Review-Chpts. P&1 MTH 140
Precalculus
Name_____________________
Simplify
each of the following.
1) 
2) 
3) 
4) 
5) 
6) 
7) A car rental agency charges $200 per
week plus $0.25 per mile to rent a car.
a) Express the weekly charge, C, as a function of the number of miles,
x.
b) How many miles can you travel in one
week for $275?
8) You inherit $10,000 with the
stipulation that for the first year the money must be invested in two stocks
paying 6% and 11% annual interest, respectively. Express the expected interest from both
investments, I, as a function of the
amount of money invested at 6%, x.
9) A 400 room hotel can rent every one of
its rooms at $120 per room. For each $1
increase in rent, two fewer rooms are rented.
a) Express
the number of rooms rented, N, as a
function of the rent, x.
b) Express
the hotel’s revenue, R, as a function
of the rent, x.
10) You have 400 feet of fencing to enclose a
rectangular lot and divide it in two by another fence that is parallel to one
side of the lot. Express the area of the
rectangular lot, A, as a function of
the length of the fence that divides the rectangular lot, x.
11) A machine produces open boxes using
square sheets of plastic. The machine
cuts equal-sized squares measuring 4 inches on a side from each corner of the sheet,
and then shapes the plastic into an open box by turning up the sides. Express the volume of the box as a function
of the length of a side of its square base, x.
12) Find the slope of the line that goes
through the given points:
a) 
b) 
13) Find
the equation of the line with a slope of –2 that passes through the point 
.
14) Find
the equation of the line that passes through the points 
.
15) Find
the slope-intercept form of the equation and then graph the equation.
16) Find the equation of the line perpendicular
to the line whose equation is 
and that passes
through the point (1,3). Give the
equation of the solid line is slope-intercept form.
17) Write the standard form of the circle
with center 
and radius 
.
18) Graph the circle:
a) 
b) 
19) Decide whether the relation defines a
function:
a) 
b) 
20) Decide whether the equation defines a
function:
a) 
b) 
c) 
d) 
21) Given that 
, find 
.
22) Find and simplify the difference quotient
, 
for the function 
.
23) Find the domain of the following
functions:
a) 
b) 
c) 
24) The number of engineers in a particular
country can be modeled by the function:
where x represents the number
of years since 1954 and 
represents the number
of engineers in thousands. How many
engineers were there in 1968?
25) Use the vertical line test to determine
whether y is a function of x.
26) Find the domain and range of the
functions graphed below. Assume that the
graphs continue on without end.
a)
26) b)
27) Graph the quadratic function 
, then use transformations of this graph to graph
. Please include a
written explanation as part of your work, using phrases like “shifted ___ units
to the ____”.
28) Graph the square root function 
, then use transformations of this graph to graph 
. Please include a
written explanation as part of your work, using phrases like “shifted ___ units
to the ____”.
29) Graph the absolute value function 
, then use transformations of this graph to graph 
. Please include a
written explanation as part of your work, using phrases like “shifted ___ units
to the ____”.
30) Given that 
31) Given that 
32) Find the functions f and g
so that 
.
33) For the given functions:
i) Find
the inverse function 
.
ii) Graph the function as a solid line or
curve and its inverse as a dashed line or curve on the same axes.
a) 
b) 
Key
