FUNCTION FAMILIES
The purpose of this program is to:
*Compare Linear, Parabolic, cubic, Square root, and absolute value functions
*Learn the effect of changing the leading coefficient on a function (dilation/reflection)
*Learn the effect of changing the values of h & k on a function (translation

Select the Parabola checkbox.Experiment with the slider for “a”, using {a|a>1}
1a. How does the change in a affect the function’s value at zero?
1b. How does increasing the value of a affect the function’s value at 1?
1c. What is true about the relationship between the new graph (red) and the old graph(black) for {a|a>1}?
Experiment with the slider for “a”, using {a|0<a<1}
2a. How does the change in a affect the function’s value at zero?
2b. How does decreasing the value of a affect the function’s value at 1?
2c. What is true about the relationship between the new graph (red) and the old graph(black) for {a|0<a<1}?
Experiment with the slider for “a”, using {a|a<0}
3. Describe the effect that it makes to the graph when a is negative.
Switch to each of the other functions one at a time & experiment with the slider for the value of a. (similar to Q1a-Q3)
4. In what ways do the other functions behave the same as the parabola?
Switch back to the basic parabola (a=1, h=0, & k=0) and experiment with the h slider, paying attention to the red equation below the word Parabola. (Note: When h is negative, it shows “minus negative” in the parenthesis but would be better written as just “plus”.)
5. Describe the relationship between the number inside the grouping symbol (i.e. parentheses) and the graph of the equation.
Switch back to the basic parabola (a=1, h=0, & k=0) and experiment with the k slider, paying attention to the red equation below the word Parabola.
6. Describe the relationship between the number outside the grouping symbol (i.e. parentheses) and the graph of the equation.
Turn on the checkboxes for the Parabola, the absolute value, and the square root. (a=1, h=0, k=0) Experiment with each of the sliders individually.
7. Watch for similarities in the behavior of the graphs of the functions. Record your observations.
8. Watch for the similarities in the equations of the functions. Record your observation.
9. Write a prediction of what the graph of y = -4|x-2|+ 1 will look like. Test your prediction. (Use a=-4, h=2,k=3)