Part 4
 Test 7
 Time: 2 hours


 For the function , determine
the:
 (h) amplitude,
Answer: 6.
 (i) period,
Answer:
 vertical shift,
Answer: 10 up.
 phase shift,
Answer:
to the right.
 domain,
Answer: all real numbers.
 range.
Answer
 Can f(t)=2? Explain.
Answer: no because the range of f(t) goes is between 4 and 16,
and since 2 is not in between those numbers, therefore f(t) can't
never be 2.
 Simplify each expression:
 .
Answer:
 .
Answer:

Answer:
 Given that and
, find the remaining five trigonometric functions
of the angle .
Answer:
 Find if . Restrict
domain if necessary.
Answer:
.
The restricted domain is .
 Find the inverse of the following function (restrict the domain
if necessary):
 If you invested $1,000 for 4 years as follows:
 Years 1 and 2 compounded weekly at 11%, and years 3 and 4 continuously at 13%.
 What simple interest rate would give you the same balance as the
above after four years?
Answer: At the end of 2 years we will have approximately
$1245.79, and at the end of 4 years we will have approximately
$1615.69.
A simple interest rate of 12.74 % pear year will yield the same
balance as the above after four years.
 Find a polynomial function that passes through the point (3,24),
has a double zero of 3 and zeros 1 and 1
 Of degree 3.
Answer: This is not possible. If 3 is a double zero, then we
have 4 zeros above. The smallest degree of a polynomial having 1, 1
and double 3 as their zeros has to be 4 according to the fundamental theorem of algebra.
 Of degree 4.
Answer:
(x3)(x3)(x+1)(x1)
or
 Of degree 6.
Answer:
There are many possible solutions for this. However all the exponents
of each of the terms must add up to 6.
 Solve for x:
Answer: The domain is restricted to all x>1.
By solving this equation algebraically we get two solutions, x=1 and
x=6, but since x=1 is not in the domain of the original equation,
then the only solution is x=6.
 Find the quadratic function whose graph contains
the points (1,2),(2,1) and (1,10).
Answer: The equation is .
 Suppose you are given a polynomial function of degree four with
a relative maximum of 10 located at x=0, a relative maximum of 22
located at x=10, and a relative maximum of 5 located at x=4. On
what interval(s) is the function:
 Increasing?
Answer: The function is increasing on the intervals
.
 Decreasing?
Answer: The function is decreasing on the intervals
.
 Give two intervals where at least one of the zeros of the
polynomial exists.
Answer:
Two intervals are and .
There are several other solutions.
If you would like to practice on exams for Parts 1, 2 or 3, click on
Menu. It will take you back to the original menu.
Fri, March 6, 1998
Copyright © 19992017 MathMedics, LLC. All rights reserved.
Contact us
Math Medics, LLC.  P.O. Box 12395  El Paso TX 79913  USA
users online during the last hour