WIR Problem Set #9 April 14, 2020 Sections 5.3–5.5, Exam 3 Review Exam 3 is this Friday, April 17, 2020! Disclaimer: while this week-in-review includes some Exam 3 review, not everything is covered on this week-in-review. Use the set of review questions in eCampus for a comprehensive review for all of Chapter 5. Also use previous Week-in-Review worksheets for more practice. Work-out Problems Study tip: Show all your work! Exercise 1. Consider the exponential function f (x)= -7e 4x . Find the domain, range, end behavior, horizontal asymptote, zeros, and y-intercept. Math 140 Week-in-Review Spring 2020 1 Nida Obatake
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WIR Problem Set #9 April 14, 2020 Sections 5.3–5.5, Exam 3 Review
Exam 3 is this Friday, April 17, 2020!
Disclaimer: while this week-in-review includes some Exam 3 review, not everything
is covered on this week-in-review. Use the set of review questions in eCampus for a
comprehensive review for all of Chapter 5. Also use previous Week-in-Review worksheets for
more practice.
Work-out Problems
Study tip: Show all your work!
Exercise 1. Consider the exponential function f(x) = −7e4x. Find the domain, range, end
behavior, horizontal asymptote, zeros, and y-intercept.
Math 140 Week-in-ReviewSpring 2020
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Exercise 2. Solve the following equations for the exact value(s) of x.
1. e2x−5 = e3 · e4
2.8−3
8−2x=
(1
42
)x· 162
3. 2x · x2 − 5 · 2x · x = 14 · 2x
Math 140 Week-in-ReviewSpring 2020
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4. 5x = 31−2x
5. log3(81)− 11log11(5) + log4(4x) = 43/2
6. logc(3x− 1) = 3, where c > 0
7. ln(x+ 1) = − ln(x) + ln(6)
Math 140 Week-in-ReviewSpring 2020
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Exercise 3. Let f(x) = 14e3x−7 and g(x) =
√log2(x)− 1, and h(x) have values in the table
given below
x -3 -2 -1 0 1 2 3 4 5 6
h(x) 0 5 0 -15 6 3 5 1 39 4
Find each of the following.
1. (g + h)(−3)
2. (fg)(√
3)
3. (f − g)(4)
4.
(f
g
)(0)
5. (f ◦ g)(x)
6. (h ◦ h)(6)
7. (f ◦ h)(3)
Math 140 Week-in-ReviewSpring 2020
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Exercise 4. Express the domain of the given function in interval notation.
1. f(x) = e4√3x−27
2. g(t) =8 · 4t
3t(2− t) 18
Math 140 Week-in-ReviewSpring 2020
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3. h(s) =55s+ 78
e12s−22
4. j(t) = log8(12− 4t)
5. h(x) =ln(x+ 15)
7√x+ 3
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Exercise 5. Aggie Venture Associates is encouraging you to deposit money into their ac-
count with an interest rate of 3.5% that compounds quarterly. How long would it take to
increase your principal to 23 times your initial investment? Round your final answer to two
decimal places, if necessary.
Reliance Reveille offers you an interest rate of 4% compounded continuously. How much
would you have to invest in the account today to have a balance of $230,000 after 40 years?
Round your final answer to two decimal places.
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Exercise 6. Let f(x) = 3
√−x+ 3
2and g(x) = x2− 4. Write down the formula of (f ◦ g)(x).
Exercise 7. Find two functions f and g such that (f ◦ g)(x) =1√
7− 2x2and neither
f(x) = x nor g(x) = x. No explanation necessary.
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Exercise 8. 1. Describe in words the transformations necessary to go from the graph of
a parent function f(x) to the graph of g(x), where g(x) = −f(x− 4) + 1.
2. The graph of f(x) is given below. On the same plane below, sketch the graph of the
following transformation: g(x) = −f(x− 4) + 1. Indicate clearly at least 6 points on
the graph of g(x).
−6−5−4−3−2−1 1 2 3 4 5 6
−5−4−3−2−1
1
2
3
4
5
•
•
• ••
•
f(x)
x
y
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Exercise 9. Use the graphs of the following parent functions to determine which are one-