HSC Extension One Maths Graphical Relationships Exam

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Important: These tests take time to write, if you’re in a position consider buying me a coffee so I can keep doing this in the long term.

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Graph of y squared equals a function of x, with multiple choice options showing different graphs labeled A, B, C, and D.
A math problem involving graphs of functions and their transformations, with four options labeled A to D showing different graphs.
Four multiple-choice graph options labeled A, B, C, and D, each displaying different linear and vertical line graphs on coordinate planes.
Mathematical exam question about functions and their graphs, including sketches of graphs and a plot of a function y=f(x).
Mathematical worksheet with graphs and equations including a graph of a function y=f(x) and a parabola h(x)=f(x)g(x), with accompanying questions and options.
A mathematical solutions page with solutions to three problems involving functions and graphs.
A page of a math textbook showing equations, explanations, and two graphs of functions, one in red and one in blue, plotted on a coordinate grid.
A page with mathematical text, equations, and two graphs. The first graph shows a parabola opening upward, with the x-axis and y-axis labeled. The second graph shows a straight line with the equation y=2x.
A mathematical explanation with a graph showing the reciprocal function, with vertical asymptotes at x = -3, -1, 2, and the graph approaching infinity near those points, and the absolute value of the function plotted as a non-negative version.
Graphs illustrating the transformation of the graph of y=|f(x)| through reflection across the x-axis, showing the original and reflected functions for positive and negative x-values.
Graph of two hyperbolas with their asymptotes and mathematical equations.
A page of handwritten mathematical equations on white paper, showing steps to solve for functions involving variables a, b, c, and expressions h(x) and g(x).

Below is a skills checklist I wrote based on the syllabus, if you can do everything listed below you should be in a good position for both your school’s graphical relationships topic test and the graphical relationships questions in the HSC.

  • Graph the reciprocal of an algebraic function, or of a graph

  • Graph trigonometric functions in radians and degrees

  • Graph absolutes of functions and functions of absolutes

  • Graph the addition and subtraction of functions which may be given in algebraic or graphical form