Given that
f(x) = ln x, x > 0
sketch on separate axes the graphs of
(i) y = f(x),
(ii) y = |f(x)|,
(iii) y = -f(x - 4) - Edexcel - A-Level Maths Pure - Question 2 - 2013 - Paper 7
Question 2
Given that
f(x) = ln x, x > 0
sketch on separate axes the graphs of
(i) y = f(x),
(ii) y = |f(x)|,
(iii) y = -f(x - 4).
Show, on each diagram, the p... show full transcript
Worked Solution & Example Answer:Given that
f(x) = ln x, x > 0
sketch on separate axes the graphs of
(i) y = f(x),
(ii) y = |f(x)|,
(iii) y = -f(x - 4) - Edexcel - A-Level Maths Pure - Question 2 - 2013 - Paper 7
Step 1
y = f(x)
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Answer
To sketch the graph of y=extln(x), note that it passes through the point (1, 0) because extln(1)=0. As x approaches 0 from the right, y approaches −extinfinity, indicating a vertical asymptote at x=0. The graph increases without bound as x increases. The equation of the asymptote is:
Asymptote Equation: x=0
Step 2
y = |f(x)|
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Answer
For the graph of y=∣extln(x)∣, the part where y=extln(x) is mirrored above the x-axis for x>1. As before, it meets the x-axis at (1, 0) and has the vertical asymptote at x=0. The graph decreases to 0 as x approaches 1, and increases thereafter. The equation of the asymptote remains:
Asymptote Equation: x=0
Step 3
y = -f(x - 4)
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Answer
For the graph y=−extln(x−4), the function is shifted to the right by 4 units. The graph crosses the x-axis at the point where −extln(x−4)=0, thus at x=5 because extln(1)=0. The vertical asymptote now is located at x=4 since extln(x−4) is undefined at that point. Therefore, the equation of the asymptote is:
