M121 Fall 95  Exam III  Nov., 1995

J4 is the only new problem for test 3 so far. Name (Print) SSN: Circle the name of your TA and Discussion Hour:

David Krebes  8 AM  11 AM
Qihui Liu:  8am  9am
Jukun Ying  9am  11 am

M121 Fall 95  Exam III  Nov., 1995

Answer all questions and SHOW ALL WORK. No credit for answers only.

Part I: Multiple choice. No partial credit but SHOW WORK! Circle the letter corresponding to

the correct answer.

1. The solution(s) to the equation

1/2 ln_{3}(x + 6) + ln_{3}(x) = 0

are: (A) 3 (B) −2 (C) 3, −2 (D) no solutions (E) 2.273

2. Find a if the point (1/8, −3) is on the graph of f(x) = log_{a}(x) (A) 1 (B) 2 (C) 3 (D) 4 (E) 5

3. The graph of y = −3 + 4 ln(x + 2) can be obtained from the graph of y = 1/x by applying

in order the following three transformations.

1. vertical stretch by a factor of a

2. horizontal shift of b units left or right 3. vertical shift of c units up or down What are the values of a, b, c and in which directions are the shifts?

(A) a =2, b=3 left, c =4 up (B) a =2, b=3 right, c =4 up (C) a =2, b= 2 right, c =3 down (D) a =2, b= 2 right, c =3 up (E) a =2, b= 2 left, c =3 down

(Partial credit) Write complete solutions and indicate your answers clearly.

M121 Fall 95  Exam III  Nov., 1995

4. The inverse of the function f(x) = 3^{2x−1} − 5 is: (A) ln_{2}(x/2 + 1))

(B) \frac{1+ln_{3}(x+5)}{2}
(C) \frac{ln_{3}(5)+1}{2}
(D) \frac{ln_{3}(5x)+1}{2}

(E) (1 + x)/2)

M121 Fall 95  Exam III  Nov., 1995

Part II : (Partial credit) Write complete solutions and indicate your answers clearly.

5 Let f(x) = − ln((x − 5)x). Sketch a complete graph of this function.

What is the domain of f?

Ans:

What is the range of f?

Ans:

What are the vertical asymptotes (if any) of f?

Ans:

What are the horizontal asymptotes (if any) of f?

Ans:

M121 Fall 95  Exam III  Nov., 1995

6. Sketch a compete graph of ln(x^{2} + 1). Tell when it is increasing or decreasing.

7. A colony of e coli contains 10,000 individuals and increases at a rate of 4