2. Consider the function f(x)=2+5log₁(2x+100) . (a) (i) Prove that_log₁x=-log₁x a 3 (ii) Show that f(x) can be written as f(x)=2-5log3[2(x+50)] . (b) The function y=f(x) is transformed from the parent function y=log3x What changes has been made to the following characteristics on y=log3x under the transformations? Explain your answers. Sketch of y=f(x) : (worths 2 out of the 10 marks) (i) The range of the function. New Range: Explanation: Original Range: (ii) The vertical asymptote. New Vertical Asymptote: Explanation: Original Vertical Asymptote:
2. Consider the function f(x)=2+5log₁(2x+100) . (a) (i) Prove that_log₁x=-log₁x a 3 (ii) Show that f(x) can be written as f(x)=2-5log3[2(x+50)] . (b) The function y=f(x) is transformed from the parent function y=log3x What changes has been made to the following characteristics on y=log3x under the transformations? Explain your answers. Sketch of y=f(x) : (worths 2 out of the 10 marks) (i) The range of the function. New Range: Explanation: Original Range: (ii) The vertical asymptote. New Vertical Asymptote: Explanation: Original Vertical Asymptote:
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Pls help ASAP, and show all work and steps and please circle the final answer.
![2.
Consider the function
f(x)=2+5log₁(2x+100) .
(a) (i) Prove that_log₁x=-log₁x
a
3
(ii) Show that f(x) can be written as f(x)=2-5log3[2(x+50)] .
(b) The function y=f(x) is transformed from the parent function y=log3x
What changes has been made to the following characteristics on y=log3x under the
transformations? Explain your answers.
Sketch of y=f(x) :
(worths 2 out of the 10 marks)
(i) The range of the function.
New Range:
Explanation:
Original Range:
(ii) The vertical asymptote.
New Vertical Asymptote:
Explanation:
Original Vertical Asymptote:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd5986c53-89d8-485d-a238-f86659e0f504%2F790f58b0-1c6f-4da5-a58a-3c6ac460ea4c%2Fdq7fek_processed.png&w=3840&q=75)
Transcribed Image Text:2.
Consider the function
f(x)=2+5log₁(2x+100) .
(a) (i) Prove that_log₁x=-log₁x
a
3
(ii) Show that f(x) can be written as f(x)=2-5log3[2(x+50)] .
(b) The function y=f(x) is transformed from the parent function y=log3x
What changes has been made to the following characteristics on y=log3x under the
transformations? Explain your answers.
Sketch of y=f(x) :
(worths 2 out of the 10 marks)
(i) The range of the function.
New Range:
Explanation:
Original Range:
(ii) The vertical asymptote.
New Vertical Asymptote:
Explanation:
Original Vertical Asymptote:
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
