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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:

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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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:
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:
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