Watch comprehensive video reviews for most units, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Transformations & asymptotes
Watch comprehensive video reviews for Transformations & asymptotes, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
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AHL 2.16
To sketch f(x)1 from f(x):
At every x-value, take the reciprocal of the original y-value: y→y1.
Points where f(x)=0 become vertical asymptotes, since 01 is undefined.
If ∣f(x)∣ is large, then f(x)1 is small (close to the x-axis). Thus, vertical asymptotes of f(x) become horizontal asymptotes at y=0. Conversely, if ∣f(x)∣ is small, then f(x)1 is large.
Local maxima and minima "flip":
a maximum at (a,b) on f(x) becomes a minimum at (a,b1) on f(x)1;
a minimum at (c,d) becomes a maximum at (c,d1). This happens because reciprocal values invert magnitudes.
Example
Sketch the graph of y=x2+2x−31.
The denominator is zero when x=1 or x=−3, so there will be vertical asymptotes there.
The quadratic x2+2x−3 has a minimum at (−1,−4), so there will me a local maxima at (−1,−41).
Since x2+2x−3 gets larger and larger y as x gets larger, there will be a horizontal asymptote at x=0.
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AHL 2.16
To sketch f(x)1 from f(x):
At every x-value, take the reciprocal of the original y-value: y→y1.
Points where f(x)=0 become vertical asymptotes, since 01 is undefined.
If ∣f(x)∣ is large, then f(x)1 is small (close to the x-axis). Thus, vertical asymptotes of f(x) become horizontal asymptotes at y=0. Conversely, if ∣f(x)∣ is small, then f(x)1 is large.
Local maxima and minima "flip":
a maximum at (a,b) on f(x) becomes a minimum at (a,b1) on f(x)1;
a minimum at (c,d) becomes a maximum at (c,d1). This happens because reciprocal values invert magnitudes.
Example
Sketch the graph of y=x2+2x−31.
The denominator is zero when x=1 or x=−3, so there will be vertical asymptotes there.
The quadratic x2+2x−3 has a minimum at (−1,−4), so there will me a local maxima at (−1,−41).
Since x2+2x−3 gets larger and larger y as x gets larger, there will be a horizontal asymptote at x=0.
Powered by Desmos