Use this applet to discover the different function transformations using graphical and algebraic representations.

Use the sliders to transform the function. Whenever you need to, you can check the green checkbox to shwo the parent function.
Begin by using the slider to adjust the value of b. What happens to the function?
Next, change the value of a. What happens to the graph of the function? What happens to the algebraic representation?
Move a back to 0 and use the slider to adjust the value of d. What happens to the graph? What happens to the algebraic representation?
Now move d back to 0 and change the value of c. What happens as c gets larger? What happens when c is close to 0? What happens when c is negative?
Practice:
First use the sliders to see a graph of the following problems.
1. A quadratic function that opens up and is shifted 3 left and 1 up.
2. A negative linear equation that has a starting value of -4 and a steepness of 4.
3. A cubic function that has a stretch of 1/2, and is shifted right 8 and down 2.
After you have practiced using the sliders to get an image of the graph, check the box at the top to show h(x). Then complete the previous problems by typing the equation into the imput bar.