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International Baccalaureate Mathematics

Functions

Syllabus Content

Determine key features of graphs.

Finding the point of intersection of two curves or lines using technology.

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

Here are some exam-style questions on this statement:

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Click on a topic below for suggested lesson Starters, resources and activities from Transum.


Furthermore

Official Guidance, clarification and syllabus links:

Maximum and minimum values; intercepts; symmetry; vertex; zeros of functions or roots of equations; vertical and horizontal asymptotes using graphing technology.

Determining the key features of graphs is crucial in the study of functions and their behaviours. These features include maximum and minimum values, which represent the highest and lowest points of the graph respectively. Intercepts are the points where the graph crosses the axes, providing crucial information about the function's behaviour at specific values. Symmetry, such as even or odd functions, offers insights into the graph's structure and repetition. The vertex is particularly important in quadratic functions, indicating the turning point. Zeroes of functions or roots of equations are the values for which the function equals zero, essential for solving equations. Lastly, vertical and horizontal asymptotes describe the behaviour of graphs as they tend towards infinity or negative infinity, respectively. Understanding these concepts is enhanced by using graphing technology, which provides a visual representation and deeper insight.

Key formulae include:

\( y = ax^2 + bx + c \) for quadratic functions, where the vertex can be found using \( x = -\frac{b}{2a} \), and the y-intercept is at \( y = c \).

For rational functions such as \( y = \frac{1}{x} \), vertical asymptotes occur where the denominator equals zero, and horizontal asymptotes are determined by the degrees of the numerator and denominator.

Example:

Consider the quadratic function \( y = x^2 - 4x + 3 \). To find the vertex, calculate \( x = -\frac{-4}{2(1)} = 2 \). Substituting \( x = 2 \) back into the equation gives the y-value of the vertex, \( y = 2^2 - 4(2) + 3 = -1 \), so the vertex is at (2, -1). The y-intercept is at \( y = 3 \), and the function has no horizontal asymptotes. The x-intercepts (zeroes) can be found by solving \( x^2 - 4x + 3 = 0 \).

If you use a TI-Nspire GDC there are instructions for finding asymptotes.

This video called GDC Tips: Intersection of Two Lines is from Revision Village and is aimed at students taking the IB Maths Standard level course

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