Chapter 1: Further graphs Notes

Sections

1. 1A Absolute value and fraction inequations Mastered

   Solve |ax + b| < k three ways (distance, algebra and graph), spot inequations with no solution, and solve inequations with x in the denominator by multiplying by its square.

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2. 1B The sign of a function Mastered

   Build a table of signs using test points around zeroes and discontinuities, and use it to solve polynomial and fraction inequations and to start a sketch.

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3. 1C Sketching reciprocal functions Mastered

   Sketch y = 1/f(x) from the graph of y = f(x): sign, zeroes and vertical asymptotes, horizontal asymptotes, turning points, domain and range.

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4. 1D Sums and differences of graphs Mastered

   Sketch y = f(x) + g(x) and y = f(x) − g(x) by adding or subtracting ordinates, including graphs with asymptotes, and find the domain of the result.

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5. 1E Graphs with absolute value Mastered

   Sketch y = |f(x)| and y = f(|x|) from the graph of y = f(x) using reflections in the axes, and see both as composites with the absolute value function.

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6. 1F Inverse relations and functions Mastered

   Form the inverse relation by swapping x and y, graph it by reflecting in y = x, swap the domain and range, handle restrictions, and use the horizontal line test.

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7. 1G Inverse function notation Mastered

   One-to-one functions, the notation f⁻¹(x), the composition test f(f⁻¹(x)) = x, restricting a domain so the inverse is a function, and where f meets its inverse.

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8. 1H Parametric equations Mastered

   Curves defined by a parameter, plotting points from parameter values, eliminating the parameter to get the Cartesian equation, parametric parabolas and circles, and restrictions.

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