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Math 1113 Final Exam Review


This review should only be used as a guide for preparation for the final exam. In
addition you should study your notes, homework, and quizzes.

Section 1

Suppose graph of f is given . Describe the following graphs relative to graph of f

ans: Vertical shrink by a factor of 1/2 units, then horizontal shift of 2 units to the

ans: Horizontal stretch of 5 units, then vertical shift of one unit down.

ans: Vertical stretch of 5 units, reflection along x-axis, then vertical shift of one
unit up.

4. Identify each translation from the function .

ans: Horizontal shrink by a factor of 1/3, horizontal shift of 2 units to the right,
vertical stretch by a factor of 5 units , reflection along the x-axis, finally vertical
translation of 2 units down.

ans: Vertical shrink by a factor of 1/4, then vertical shift of 3 units up.

ans; Vertical stretch of 2 units, reflection along x-axis, then vertical translation
of 1 unit up.

Find the domain of each function.
5. ans:

6.  ans:

7. ans:

Evaluate the indicated functions, where and

8. ans: 0
9. ans: − 25/7

Find f ◦ g for the given functions f and g.

10. ans:

11. ans:

Find inverse of each function.

12. ans:

13. ans:

14. Given and find then determine
domain of f ◦ g.
ans: Domain

15. Given  find   then determine domain of f ◦ g.
ans: Domain

Also you should know how to:

a. Identify intervals that a given function is constant, increasing, or decreasing.
c. Identify the domain and range of a graph of a function .
d. Find inverse of a function given its graph.
e. Use the horizontal and vertical line tests .
f. Find equation of a function given its graph.
g. Distinguish between vertical and horizontal stretch and shrink.

Section 2

1. Find the intercepts of the graph of each function.

a. ans: x-intercept: y-intercept:
b. ans: x-intercept: y-intercept:

2. Identify any vertical and horizontal asymptotes of the following functions.

a. ans: vertical asymptote: none ; horizontal
asymptote: y = 3

b. ans :vertical asymptote: x = −1 ; horizontal
asymptote: none

c. ans: vertical asymptote: x = 3 ; horizontal
asymptote: y = 0

3. Find intercepts of each rational function .

a. ans: x-int = 0, y-int = 0
b. ans: x-int = −1, 5/3 ; y-int = −5

Also you should know:

a. The difference between rational and polynomial functions .
b. What are zeros of a polynomial functions, and how to find them. How to find
multiplicity of a zero .
c. Even and odd functions
e. How to find average rate of change of functions between two given points.

Section 3

Solve for x (# 1-8).
1. ans:x ≈ 3.55
2. ans:x = 3.71
3. ans:x ≈ 0.69
4. ans: x = 1
5. ans: x = 4
6. ans: x = 103
7. ans: No solution
8. ans:

Write the expression as a logarithm of a single quantity.

9. ans:
10. ans:

11. Find domain of   ans:
12. Find domain ofans:
13. Find domain of ans:

Use your graphing utility to sketch the graph of each function, then state the
domain, range, intercepts and asymptote of f.

ans: Domain: ; Range: ; x-int: none ; y-int: ; asymptote:
y = 2

ans: Domain: ; Range: ; x-int: ; y-int: ; asymptote:
x = −2

16. How long will it take for $2500 to triple if it is invested in a savings
account that pays 4.5% interest compounded continuously ?
ans: approx 24 years

17. Suppose $3000 is invested into an account paying 6% interest
compounded quarterly. Find the balance in the account after 5 years.
ans: $4040.56

18. The population of a town is modeled by where t = 0
represents the year 2000. According to this model, when will the population
reach 18,000?
ans: year 2615

19. Radioactive stronium decays according to the function ,
where t is time in years.

a. If an initial sample contains y0 = 5 grams of radioactive stronium, how many
grams will be present after 60 years?
b. What is the half-life of radioactive stronium?
ans: a. 1.19 grams   b. 29 years

20. The half-life of a certain radioactive material is 1200 years.
a. Find the decay constant k. ans: −0.000577
b. What percent of material will remain after 135 years. ans: 92%

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