Transformations: Basic Family of Functions
- Author:
- Auston B Cron
- Topic:
- Cosine, Function Graph, Sine
In this activity you will use a slider to change the basic (parent) functions. You will be able to change value of the sliders , , h, and k to transform the function by moving these sliders. The and allow your to reflect outside and inside of the function change you results. There are two check boxes to permit the user to easily demonstrate the results of a vertical or horizontal line test. The and the represent the effects of multipliers outside of the function f(x) and inside the parenthesis of f(x), sometimes these multipliers when used separately produce the same graph. When or are zero, the resulting graph is a constant function.
[Note: you may need to move a panel right to about 10 on x-axis.]
[Note: you may need to move a panel right to about 10 on x-axis.]Your job is to determine the effects of each of the sliders on parent functions.
a) What does do to each function? Hint: its effects are the same for all functions.
b) What does do to each function?
c) What does h do in each function?
d) What does k do in each function?
e) What does do in each function?
f) What does do in each function?
g) Which axis is effected by the blue sliders?
h) Which axis is effected by the red sliders?
Use these handouts as a guide to analyze the included functions.
Student worksheet (Original) PDF DOCX DOC.
Graph sketching guideline worksheets Algebra II/Regular Precalculus PreCalculs/Calculus (two templates per page)
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This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers as a worksheet to be completed for a grade.