MATH 002 Exam 3D: Square Root Function and Rational Exponents, Exams of Mathematics

The solutions to exam 3d for math 002, focusing on the square root function and rational exponents. It includes instructions, graph transformations, numerical expressions, and graph analysis. Students are required to show their work and provide exact answers.

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Pre 2010

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MATH
002
EXAM
#3D
Square
Root
Function
and
Rational
Exponents
Wednesday,
November
12,
1997
NAME:_____
โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”Disc,
time:_
INSTRUCTIONS:
Please
show
all
work
in
order
to
receive
any
partial
credit.
Unless
otherwise
specified,
give
exact
answers
in
simplified
form,
i.e.,
do
not
use
decimal
approximations.
BOX
your
final
answers.
[19]
1.
Use
the
function
below
to
answer
the
following
questions.
y
=
\Jx
+
3
โ€”
4
[4]
a.
Describe
the
shifts
of
the
basic
square
root function's
graph
that
are
necessary
in
order
to
obtain
the
graph
of
the
function
above.
Horizontal
shift:_____โ€”
โ€”
___
Vertical
shift:_______.
[2]
b.
What
is
the
starting
point
of
the
function
above?
Starting
point:
[2]
c.
What
is
the
yโ€”
intercept,
if
any,
of
the
function
above?
yโ€”
[4]
d.
What
is(are)
the
:r-intercept(s), if
any,
of
the
function
above?
x-
-o
[3]
e.
Graph
the
function
in
the
space
provided
and
LABEL
all
points
that
you
found
above
x
>
-3
[2]
f.
What
is
the
domain
of
the
function
above?
Domain:______________
y
โ€ข>
-y
[2]
g.
What
is
the
range
of
the
function
above?
Range:โ€”โ€”โ€”'_________
pf3
pf4

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MATH 002 EXAM #3D

Square Root Function and Rational Exponents

Wednesday, November 12, 1997 NAME:_____ โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”Disc, time:_

INSTRUCTIONS: Please show all work in order to receive any partial credit. Unless otherwise specified, give exact answers in simplified form, i.e., do not use decimal approximations. BOX your final answers.

[19] 1. Use the function below to answer the following questions.

y = \Jx + 3 โ€” 4

[4] a. Describe the shifts of the basic square root function's graph that are necessary in order to obtain the graph of the function above.

Horizontal shift:_____โ€” โ€” ___ Vertical shift:_______.

[2] b. What is the starting point of the function above? Starting point:

[2] c. What is the yโ€” intercept, if any, of the function above? yโ€”

[4] d. What is(are) the :r-intercept(s), if any, of the function above?

x- -o

[3] e. Graph the function in the space provided and LABEL all points that you found above

x > -

[2] f. What is the domain of the function above? Domain:______________

y โ€ข> -y [2] g. What is the range of the function above? Range:โ€”โ€”โ€”'_________

[9] 2. Rewrite each numerical expression in radical form and then evaluate, if possible, without using a calculator.

[3] a. (-

[3]b. i 3 =

ยฃ

[3] c. -27-i = 3

)

2.

H-i)

[12] 3. Simplify each of the following expressions, rationalizeStlfappropriate~aenominators, and write your final answer without negative exponents. Assume that x > 0 and y > 0.

[3] a.

= Z X V A

\TxT-3v ]

li

-3*

9 X

y

[10] 5. The velocity, v, in feet per second of a rolling ball as a function of time, t, in seconds, is given by

[2] a. What is the initial velocity of the ball? Initial velocity:.

[3] b. How long does it take the ball to come to rest? Time to rest:..

[3] c. At what time is the velocity of theHjall one-third of its original velocity?_

[2] d. How fast is the ball travelling at 6 seconds? Velocity at 6 sec:โ€”_______