Reflecting, Stretching and Shrinking Graphs What does equation look like to do these transformations

Translation Review What did we do to the equation to move the graph up and down What did we do to the equation to move the graph left and right Notice that the sign does the opposite movement, this has something to do with we are affecting the independent variable before we do some of the operations The basic idea you see here should work with all of the parent functions that we discussed

Vertex With translations we talked about the vertex of the parent function – this is the (h,k) value in the equation. Look for the new location of the vertex to determine the movement, look for the (h,k) value in the equation to determine the movement

Example What is the parent function? Describe the movement? What is the new function for this graph?

Example Look at the function equation. Describe the translation of the function.

Reflection Play around with the quadratic equation. How would you get a mirror image of the parent function about the x axis Play around with the square root equation How would you get a reflection of the parent about the x axis and y axis

Reflection Some parent functions are symmetric around the y axis, quadratic and absolute value so you can’t reflect them about the y-axis To reflect a graph about the x axis you put a negative sign in front of the equation, this takes the opposite of everything you originally had To reflect graphs about the y axis you put the negative sign inside the function

Reflection The value in front of the function is a If a is positive it is not flipped If a is negative it is flipped

Stretch and Shrink Stretch – have the graph grow quicker Shrink – have the graph grow slower Object – think of a scale factor you would use to affect all the points Play around on your calculator to determine what would make a function stretch or shrink, use the quadratic function, does the ideas you found work for all the functions

Stretch and Shrink If you noticed affecting the number before the function, this is a, makes the graph stretch or shrink |a|>1 stretch or grow quicker 0<|a|<1 shrink or grow slowly

Example

General equation with all Transformations

Homework Pg 449 3,5 Pg 456 2,3,5,11 Pg 467 1-3, 9, 10

To Find A You need the vertex and another point on the graph Sub in values into the equation for h,k,x and f(x) then solve for y The graph should give you a point you can determine for x and y

Example Vertex ( 3,1) Pt (0,7) or (6,7)

Reflecting over a line not the x or y axis Reflect is graph about the x or y axis Then translate the graph twice what the line of reflection is Most graphs are reflected about the y-axis the take the opposite of the function and then add twice the distance of the line of reflection