[b][size=150]The absolute value function is [color=#6aa84f]y = |x|[/color] , denoted by function g. [br][br][/size][/b]The transformed basic function is [color=#ff0000][b]y = a|x - h| +k[/b][/color].[br][br][b][color=#ff0000][size=150]Note[/size][/color][/b]: The 'slider' feature on the x-y coordinate plane can be used to change the [b][color=#3c78d8]a[/color], [color=#9900ff]h[/color], and [color=#ff00ff]k[/color][/b] values [br] for the following exercises. To do so, place the cursor and hold it on the dot of the slider and [br] slide it to the desired m and b values.[br] To move the slider to a different location on the x-y plane, place the cursor and hold it on the line [br] of the slider and move it to the desired location.[br][br][b][color=#ff00ff]Note: You can zoom in or out with the mouse.[/color][/b]
[b]Use the slider to change the value of [color=#9900ff]h[/color]. What do you notice?[/b]
[b]Use the slider to change the value of [color=#ff00ff]k[/color]. What do you notice?[/b]
[b]Use the slider to change the value of [color=#1155cc]a[/color]. What do you notice?[/b]
[b]Use the sliders to graph the function f(x) = |x + 3| - 5. [br]How does this compare to the graph g(x)=x?[/b]
translates 3 units left and 5 units down
[b]Use the sliders to graph the function f(x) = |x - 4| + 2. [br]How does this compare to the graph g(x)=x?[/b]
translates 4 units right and 2 units up
[b]Use the sliders to graph the function f(x) = 2|x - 3| + 4. [br]How does this compare to the graph g(x)=x?[/b]
graph narrows (vertical stretch), translates 3 units right and 4 units up[br]
[b]Use the sliders to graph the function f(x) = -0.2|x - 6| + 3. [br]How does this compare to the graph g(x)=x?[/b]
graph widens (vertical compression) & reflects vertically, translates 6 units right and 3 units up