Hidden Functions

Work Window

Hidden functions can be used to develop intuition about the algebraic representation of functions. The objective of this activity is for the student to find the algebraic expression for the hidden function. Students can do the following to help them find the hidden expression:

Plot the function.
Change the plot viewing window by changing the plotting domain and range.
Use the Single Root Finder tool on the Tool Palette to find the roots of the plotted function.
Use the Rectangular Tracker tool on the Tool Palette to evaluate the hidden function for any value of x.
Note: To find the value of the function at an exact value of x, enter the x-value into the Domain & Range window and click the Enter button or press the Enter key.
Use the Coordinate (Point) tool on the Tool Palette to place a point on the plotted curve along with its coordinates.
Note: You must select (x, y) from the Coordinate (Point) tool's pop-up menu to display the coordinates of the point.
Use the Maximum/Minimum Finder tool on the Tool Palette to find the maximum and minimum values of the plotted function.
Use the Line Segment tool on the Tool Palette to measure the distance between points or to measure the slope of a line segment.
Use the Tangent tool on the Tool Palette to find the slope of the tangent line to the curve at a point.

When you think that you have found the hidden function expression:

Select New Function from the Work menu and enter your expression for the hidden function.
Select Overlay Plot from the Graph menu to see how your function expression matches the hidden function expression.

Try to find as many hidden function expressions that you can.

Note: Function expressions can be hidden or shown by selecting either Hide Function or Show Function from the Options menu. Also, you can set a password so that only you can show hidden functions and not your students. See TEMATH's Help system for more information on hiding and showing function expressions.

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