Name
Date
Are You Ready For Precalc?
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Part 1: No calculators allowed (1–11)
You should have transformed parent functions by
dilation and translation.
1. Describe verbally and algebraically what
transformation was applied to the dashed graph, f,
to get the solid graph, g.
4.
Explain how to find all asymptotes of a rational
function
5.
Explain why there cannot be oblique AND
horizontal asymptotes when graphing a rational
function.
6.
Write the general equation for a(n)
• Exponential function
• Power function
Words:
Equation:
2. In precalculus you have used angles to measure
rotation, so the angles can be greater than 180˚ or
negative. Sketch an angle of 210˚ in standard
position in a uv-coordinate system. Mark the
reference angle and write its measure. Write the
exact value (no decimals!) of cos 210˚.
• Logarithmic function
7. Sketch the graph of a
• Logistic function
• Quadratic function
8. Draw and label, from memory, the unit circle
including all appropriate measures and labels.
3. You apply transformations to a sinusoid, an
example of a periodic function. Sketch one cycle
of this sinusoid. Show coordinates of high and
low points and upper and lower bounds. (you
need to know how each constant in the equation
transforms the parent function y = cos 
y = 5 + 2 cos 3( – 20˚)
9. Suppose that a computer software company has
30 programmers. Use factorials to write the
number of different ways they could select a
group of 6 of the programmers to work on a
particular project.
15. Making a mathematical model involves finding
the particular equation. Find an equation for the
sinusoid for which a half-cycle is shown here.
SCALE IS OFF!
10. Given A and B are independent events with
probabilities P(A) = 0.9 and P(B) = 0.8, find the
probability that A or B occurs.
11. Given that the probability of event C is 0.3 and
the payoff is $10 if C occurs and –$2 if C does
not occur, find
• P(not C)
• The mathematical expectation
Part 2: Graphing calculators allowed (12–44)
To apply sinusoids to real-world problems, you
defined circular functions, with the help of radians.
12. Show how the x-axis is wrapped around the unit
circle to define an angle of 2 radians.
16. Dilations and translations have special names
when applied to sinusoids. For the graph in
Problem 15 give the:
• Amplitude
• Period
• Phase displacement (for cosine)
• Sinusoidal axis location
Tide Problem (17–20): The depth of water at the
seacoast is a periodic function of time due to the
motion of the tides. Suppose that the depth y, in feet,
is given by
y = 3 + 4 cos

5.7
( x  2)
where x is time in hours after midnight last night.
17. At what time did the first high tide occur today?
How deep was the water at that time?
18. What is the period of this function?
19. When does the second high tide occur today?
13. How many degrees are there in 2 radians?
14. Write the exact number (no decimals!) of radians
in 90˚.
20. The tide is completely “out” when the depth
calculated for the water is zero or less. Between
what two times is the tide first completely out
today? Show how you get your answer.
Dog’s Weight Problem (21-24): As dogs of a
particular breed grow, their weight is a function of
their length. Suppose that these lengths and weights
have been measured.
x (in.)
y (lb)
6
2
12
14
24
98
29
170
34
260
37
330
21. What pattern do the first three data points follow?
What type of function has this pattern?
22. Find the particular equation for the function in
Problem 21.
23. Use the appropriate kind of regression to find the
function of the type in Problem 21 that best fits
all six data points. Write the correlation
coefficient, and explain how it indicates that the
function fits the data quite well.
Weight-lifting Problem (25–28): Emma Strong starts
an exercise routine to build up her muscles. She
measures her progress at the end of each week, x, by
the number of pounds, y, she can lift (see the table and
graph).
x (weeks)
1
2
3
4
5
6
7
y (lb)
14
18
24
31
40
49
60
25. What graphical evidence is there that an
exponential function might fit the points? Based
on endpoint behavior, why would a logistic
function be more reasonable?
26. Write the particular equation of the best-fitting
logistic function. Use the equation to predict the
weight she can lift after week 15.
24. Use the regression equation from Problem 23 to
predict the weight of a newborn puppy 4 inches
long. Which do you use, interpolation or
extrapolation, to find this? How can you decide?
27. Plot the logistic function. Sketch the result on the
given figure. Show the upper horizontal
asymptote and the point of inflection.
28. What limit does the number of pounds approach?
Flower Pot Problem (29–30): A precalculus class
reasons that the height, h, in centimeters, of a stack of
flower pots should be a linear function of the number
of pots, p, in the stack. They measure the data shown
in the table and point plot. FIX SCALE!
Logarithmic Function Problems (31–34):
31. Use the definition of logarithm to evaluate y =
log7 41.
32. Use the log of a power property to solve this
exponential equation: 52x = 157
p (number
h (cm)
of pots)
1
10.5
2
13.2
3
16.0
4
18.7
5
21.3
6
23.9
7
26.5
8
29.1
9
31.6
10
34.1
29. Write the linear regression equation, and give
numerical evidence from the regression result that
a linear function fits very well.
30. Use the regression equation to predict the height
of a stack of 20 pots. Why is this not twice the
height of a stack of 10 pots?
33. Use the change of base property to evaluate
log891 using natural logarithms.
34. Plot the graph of f(x) = ln x. Sketch the result.
Explain why f(1) = 0. Give numerical evidence to
show how f(4) and f(6) are related to f(24).