Using Desmos to Explore Transformations of the Families of Functions Name: ______
Objective 3: I can identify the effect of transformations of a graph when given the equation.
1. Log on to your account and go to the web browser. Type in the following web address for the graphing calculator we will be using:
https://www.desmos.com/calculator
2. On the left hand side of the screen, type in: f(x) = x and push enter.
3. On the next line, type in g(x)=a*f(b(x – h) )+ k. On the line below it asks about sliders. Select “All”. It should now look like the screen below. Change the slider numbers to those shown.
4. Change the value of a. Explain what this does to the graph:
5. Set a back to 1. Now change the value for b. What does this do to the graph?
6. Set b back to 1. Now change h. How does this change the graph?
7. Set h back to 0. Now change k. How does this change the graph?
8. Pick another parent function. Change your f(x) to one of your other parent functions. Do the sliders again. Are the changes significantly different? Describe anything you notice:
Translation:
Dilation - Vertical Stretch:
Dilation - Vertical Shrink:
Reflection:
10. Given any function, describe the effects of the following parameters on the function f(x) : y = a*f(b(x – h)) + k
Parameter a / Parameter b / Parameter h / Parameter k
|a| > 1 / b > 0 / h > 0 / k > 0
0 < |a| < 1 / b < 0 / h < 0 / k < 0
a < 0 / b = 0 / h = 0 / k = 0
a = 0
11. Given the following functions, describe the transformations on the parent function, f(x). Use the vocabulary: translation, stretch, shrink, reflection.
a. a. f(x) = x2; h(x) = 3(x – 4)2 + 2
b. b. f(x) = x3; g(x) = –(x – 1)3
12. Write the equation of the function given the following transformations, check your answer by graphing in Desmos.
a. a. The graph of is reflected over the x-axis, vertically stretched by a factor of 2, and translated vertically down 1 unit.
b. b. The graph of f(x) = |x| is translated horizontally to the left 3 units and translated vertically up 5units.