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Solving Equations Involving the Modulus function, Composite Functions and Examining the Range of a Function
This question is made up of four parts. Students are required to sketch the graph of a modular function, find where this function intersect a line, find the value of a composite function and find the range of a quadratic function.
The mathematical solution explains how to sketch the modular function by first drawing the straight line and reflecting appropriately in the x-axis. Explanation is then given as to which equations need to be solved to find the points of intersection of the two lines. The value of the composite function fg(2) is then found where g(x) is a quadratic function and f(x) is the function containing a modulus. The range of the quadratic function, in the given domain, is then found by locating the maximum and minimum values in this domain.
Graphical solution 1 explains how to use the graphic calculator to use the 'abs' function to draw the graph of a function containing a modulus. The second line is then drawn and the points of intersection are found.
Graphical solution 2 explains how input a composite function into the graphical calculator to find the value of fg(2). The second part explains how to limit the domain when drawing the graph of a function then find the maximum and minimum function.
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