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.
The video will automatically pause when it reaches a problem.
AHL 2.16
To sketch [f(x)]2 from f(x):
Square all y-values: for each x, the new y-value is (f(x))2.
Because y2≥0, the entire graph of [f(x)]2 is on or above the x-axis.
Points where f(x)=0 remain on the x-axis.
Any minima below the x-axis become maxima above the x-axis.
Any maxima below the x-axis become minima above the x-axis.
If ∣f(x)∣<1, squaring makes it closer to 0; if ∣f(x)∣>1, squaring makes it larger.
Negative parts of f(x) become positive when squared, so everything below the x-axis is reflected above it, with the magnitude of y-values adjusted according to the square.
Powered by Desmos
Notice the "rounded corners" where the function touches the x-axis, as opposed to the sharp corners for ∣f(x)∣.
AHL 2.16
To sketch [f(x)]2 from f(x):
Square all y-values: for each x, the new y-value is (f(x))2.
Because y2≥0, the entire graph of [f(x)]2 is on or above the x-axis.
Points where f(x)=0 remain on the x-axis.
Any minima below the x-axis become maxima above the x-axis.
Any maxima below the x-axis become minima above the x-axis.
If ∣f(x)∣<1, squaring makes it closer to 0; if ∣f(x)∣>1, squaring makes it larger.
Negative parts of f(x) become positive when squared, so everything below the x-axis is reflected above it, with the magnitude of y-values adjusted according to the square.
Powered by Desmos
Notice the "rounded corners" where the function touches the x-axis, as opposed to the sharp corners for ∣f(x)∣.