5 homework of Math 1001

MATH 1001: Pre-Calculus Mathematics 1

TRU Open Learning

Assignment 4: Exponential and Logarithmic Functions (80 marks, 8%)

Complete the following questions from the textbook. Show all your work, as full credit

will not be given for inadequately explained answers. This assignment is worth 8% of

your final grade and will be marked out of 80. For detailed instructions on how to

submit your assignments go to “How to Send Assignments for Grading” in your

Course Guide.

Section 4.1

1) Page 259, Q. 20 [4 marks]

2) Determine the domain and range of 𝑓 −1 for 𝑓(𝑥) = 5𝑥−2

3𝑥+1 without actually

finding 𝑓 −1. [4 marks]

3) Find the inverse of 𝑓(𝑥) = 4𝑥+5

2𝑥−3 . [4 marks]

4) Page 260, Q. 54 [4 marks]

Section 4.2

5) Sketch the graph of 𝑓(𝑥) = ( 9

4 )

𝑥

+ 3. [4 marks]

6) Find an exponential function of the form 𝑓(𝑥) = 𝑏 𝑎𝑥 + 𝑐 that has the following

graph. [5 marks]

7) Page 270, Q. 40 [4 marks]

2 Assignment 4

TRU Open Learning

Section 4.3

8) Use the graph of 𝑦 = 𝑒 𝑥 to help sketch the graph of 𝑓(𝑥) = 2𝑒 −3𝑥. [4 marks]

9) Find the zeros of 𝑓(𝑥) = 𝑥4𝑒 −2𝑥 − 8𝑥𝑒 −2𝑥. [3 marks]

10) Page 281, Q. 28 [4 marks]

Section 4.4

11) Solve the equation log5 𝑥 2 = −2. [4 marks]

12) Solve the equation 𝑒 −3 ln 𝑥 = 1

27 . [4 marks]

13) Sketch the graph of 𝑓(𝑥) = ln(𝑥 − 2𝑒). [4 marks]

14) Page 296, Q. 72 [4 marks]

Section 4.5

15) Write the expression 4 log(𝑦4𝑥−2) − 3 log ( 𝑥3

𝑦2 ) + 5 log(𝑥2 √𝑦3

5 ) as one

logarithm. You do not need to simplify your answer. [4 marks]

16) Page 303, Q. 26 [4 marks]

17) Page 303, Q. 34 [4 marks]

Section 4.6

18) Page 313, Q. 24 [4 marks]

19) Solve the equation log √𝑥2 + 1 3

= 1

3 without using a calculator. [4 marks]

20) Page 314, Q. 36 [4 marks]

Select questions associated with the following course textbook are used with

permission from Cengage Learning:

Swokowski, E. W., & Cole, J. A. (2012). Precalculus: Functions and graphs

(12th ed.). Belmont, CA: Brooks/Cole, Cengage Learning