# Math 1113 Final Exam Review

**Rouhani**

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

(#1-3).

1.

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

left

2.

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

3.

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

unit up.

4. Identify each translation from the function .

a.

**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.

b.

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

c.

**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.

14.

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

y = 2

15.

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 y_{0} = 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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