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 3 - 2013 - Paper 7
Question 3
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 point... 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 3 - 2013 - Paper 7
Step 1
i) y = f(x)
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Answer
The graph of y = f(x) = ln x is defined for x > 0. The graph passes through the point (1, 0) and approaches negative infinity as x approaches 0 from the right. The vertical asymptote is the y-axis (x = 0).
Key points:
x-intercept: (1, 0)
Asymptote: x = 0
Step 2
ii) y = |f(x)|
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Answer
The graph of y = |f(x)| reflects any negative values of f(x) above the x-axis. For ln x, this means the segment of the curve that falls below the x-axis (for x in (0, 1)) will be flipped.
Key points:
x-intercept: (1, 0)
Asymptote: x = 0 (remains the same as f(x))
Step 3
iii) y = -f(x - 4)
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Answer
This graph translates the graph of f(x) = ln x horizontally to the right by 4 units and reflects it over the x-axis. The point (4, 0) will be on this graph.
