find the following:
- Amplitude,
Answer: 10. - Period,
Answer:
.
- Horizontal Shift (phase shift),
Answer: 3 to the left. - Vertical Shift,
Answer: 10 down. - Domain,
Answer: The set of all real numbers, or in interval notation,
.
- Range,
Answer: The range is all values of y between 0 and -20, or in interval notation, [-20,0]. - and four points that have a y-coordinate of 0.
Answer: Here are four such values of x that have a y-coordinate of 0:
There are infinitely many other solutions.
is located on the
terminal side of the angle t, find a point on the terminal side of
the following angles:
-
Answer: (-0.125,-0.375) -
Answer: (-0.125,-0.375) -
Answer: (-0.125,0.375) - -t
Answer: (0.125,-0.375)
as an algebraic expression in x.
Answer:
- Convert
to radian measure.
Answer: 2.2453 radians. - Convert 128.3842 radians to degree measure in the
format.
Answer:
- The graph of
is bounded by what two functions?
Answer: The graph of f(x) is bounded by the functions
,
and 
.
- Why are these two lines considered boundary functions?
Answer: Because the greatest value
can be is 1, and the
lowest value it can be is -1. Therefore, the graph of f(x) is
contained between the functions , and . - Graph the function and the two boundary functions.
Answer:
Answer: The buildings are approximately 4704.63 feet apart.
- Restrict the domain of the function
to an
interval where the function is increasing, and,
Answer: The biggest interval which will work is
.
- Determine
over that interval.
Answer:
- Then sketch the graphs of both f and
on the same
coordinate system.
Answer:
- What relationship do the graphs of these two functions have to
the graph of the function g(x)=x?
Answer: The graph of
is a reflection of the graph of
f(x) over the line g(x).
Answer: The interest earned will be $23,201.17.
Answer: The solution is the set of all x's on the intervals
- When does
.
Answer: When the value of x is greater than 0, x>0. - When does
.
Answer: Both functions are equal when x>0.
, where t time is given in years and
t=0 corresponds to the year 1900.
- In what year was the population 60,000?
Answer: It was 60,000 in the year 1915. - Did the population ever reach 1,000,000?
Answer: It was 1,000,000 in the year 1977. - How long will it take for the population to reach 10,000?
Answer: The population will never decrease as long as the same growth behavior continues.
.
- algebraically.
Answer: There must be six (real or complex) zeros since this is a sixth degree polynomial. Using the rational zero test, and synthetic division to find the rational zeros, one obtains as zeros:
- graphically-explain how you interpreted the graph to arrive at
your answer.
Answer:
, and z:
Answer: 