This is a MATH 128 final TEST please print out the test and write your answers on it and scan it back to me.

If there’s any questions please let me know.

BCCC

MAT 128

Summer 2020

Professor: Ray Orocco-John

Student’s Name: ________________________________________________

Final Exam

Show all work. Answers without adequate justification will not receive full credit. Solve problems

algebraically whenever possible. Simplify to the lowest terms.

1) (3pts) Match the graphs with the equations.

y = log x

y = ln x

Letter ________

E

F

D

C

Letter _________

B

y=2

x

y = 3x

A

Letter _________

Letter _________

y = (0.4) x Letter _________

y = ex

Letter _________

2) (8pts) Fill in the following table:

Function

y-intercept

Growth or decay rate

(0, 20)

Growth or

decay?

Decay

(0, 5)

Growth

7% continuous rate

6% annual rate

y = 13(1.4) x

y = 17e 0.35 x

3) (4pts) Granny wants to start a college account for her newborn granddaughter. How much money does she

need to deposit now into an account earning 3% compounded quarterly so it will be worth $20,000 in 18

years?

4) (8pts) The population, P, of a group of rabbits t years after being released in a new habitat is given by

t

P (t ) = 500 (1.03)

a) How many rabbits were initially released?

b) Fill in the blank: The rabbit population is growing by _____% per year

c) How many rabbits will there be in 2 years?

d) When there will be 600 rabbits?

5) (6pts) Solve the following for x.

a) 2log3 ( 2 x − 3) = 4

b) 3(4) x+2 = 21

c) 4e12 x + 3 = 19

6) (5pts) Find a formula for an exponential function such that f(1) = 3 and f(-1) = 12

7) (2pts) Rewrite as a single logarithm: 2 log( x) + 3 log( y ) − log( z )

8) (2pts) Solve for x. log( x + 48) + log( x) = 2

9) (4pts) Bismuth-214 has a half-life of 20 minutes. What percent of the original amount is left after one hour?

10) (5pts) In 2003, there were 7225 Starbucks stores. In 2005, there were 10,241 Starbucks stores. If Starbucks

continues to increase exponentially at the same rate find the doubling time.

11) (7 pts) Given P( x) = 3( x − 1)2 ( x + 1)( x + 2) answer the following (you do not have to multiply this out)

a) What is the leading term of P(x)? _____________

b) What is the degree of P(x)?

_____________

c) As x → the function P ( x ) → _______________

d) As x → − the function P ( x ) → _______________

e) How many turning points (bumps) does it have? ______________

f) Write the coordinates of the x-intercept(s) _____________________________

(indicate if they are single/ double / triple etc..zeros)

g) Find the coordinates of the P-intercept(s) ______________________________

show work algebraically

12) (5 pts) Given the graph below write the equation for G(x).

G(x)

(show work to find the value of the constant, a)

x

13) a. (5 pts) Given the graph below, what is the equation?

H(x) =

(show work to find the value of the constant, a)

x2 − 7

b. (2 pts) Where is the horizontal asymptote (if any) of n( x) =

. Explain.

6x − 2×2

14) (7 pts) Given: J(x) = -12 (x – 1)

(x + 3) (x – 2)2

a) What are the coordinates of the x-intercept(s)? _________________________________

b) What are the coordinates of the j-intercepts(s)? _________________________________

c) Where are the vertical asymptotes (if any)? ____________________________________

d) Where are the horizontal asymptotes (if any)? __________________________________

e) As x → , j ( x) → _______________

f) As x → − , j ( x) → _______________

g) Graph the function & its important features.

x

15)(6pts) Given the function f ( x) = 3 x + 2 − 4

a. Algebraically find the coordinates of the vertical intercept

b. Algebraically find the coordinates of the horizontal intercept(s)

c. What is the Range of this function?

16) (5pts) Find the domain of g(x). Find the domain & range of f(x), the interval on which f(x) is decreasing,

and the interval on which f(x) is concave up. Write your answers in interval notation.

x−2

a. g ( x) =

Domain of g(x)____________________

x−4

f(x)

b)

Domain of f(x) ______________________

Range of f(x) _______________________

f(x) is decreasing on: __________________

f(x) is concave up on: __________________

17) (6pts) The following graph is made from pieces of three transformed toolkit functions. Write a

piecewise defined function that describes the graph.

__________________________ if _______________

f ( x) = __________________________ if _______________

__________________________ if _______________

18) (5pts) Given g ( x) = 5 x − x 2 , evaluate & simplify

a) g ( −3)

b) g ( x + 2)

19) (4pts) Write the letter in the space provided that BEST describes the function over the entire domain.

i)_______ The rate of change is 0

A) An increasing linear function

ii)______ The rate of change is undefined

B) A decreasing linear function

iii)______ The rate of change is < 0
C) A Horizontal Line
vi)______ The rate of change is > 0

D) A Vertical Line

20) (5 pts) List and explain all asymptotes (if any) of M(x) = 2×2 + 3x – 5

x+2

a. Vertical Asymptotes

b. Horizontal Asymptote

c. Oblique Asymptote