Chapter 2.5 Transformations of functions and graphs v2

# Multiply rhs by 2 y 2 x 2 stretch vertically by

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Multiply RHS by 2 y = 2 x 2 Stretch vertically by factor of 2. Stanley Ocken Math 19500 Precalculus: Transformations of functions and graphs

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Transforming equations and graphs Transforming graphs of functions Sample problems Examples: Six function transformations -6 -4 -2 0 2 4 6 -4 -3 -2 -1 0 1 2 3 4 X Y y = x 2 y = x 2 2 Transforming the equation of the parabola y = x 2 : Result is another parabola. Original graph y = x 2 is red. Each time you click, the transformation on the last line below will produce the blue graph at the left. If you: y = x 2 becomes Effect on graph Add 2 to RHS y = x 2 + 2 Move UP 2. Subtract 2 from RHS y = x 2 - 2 Move DOWN 2. Multiply RHS by 2 y = 2 x 2 Stretch vertically by factor of 2. Divide RHS by 2 y = x 2 2 Shrink vertically by factor of 2. Stanley Ocken Math 19500 Precalculus: Transformations of functions and graphs
Transforming equations and graphs Transforming graphs of functions Sample problems Examples: Six function transformations -6 -4 -2 0 2 4 6 -4 -3 -2 -1 0 1 2 3 4 X Y y = x 2 y = - x 2 Transforming the equation of the parabola y = x 2 : Result is another parabola. Original graph y = x 2 is red. Each time you click, the transformation on the last line below will produce the blue graph at the left. If you: y = x 2 becomes Effect on graph Add 2 to RHS y = x 2 + 2 Move UP 2. Subtract 2 from RHS y = x 2 - 2 Move DOWN 2. Multiply RHS by 2 y = 2 x 2 Stretch vertically by factor of 2. Divide RHS by 2 y = x 2 2 Shrink vertically by factor of 2. Multiply RHS by -1 y = - x 2 Reflect across x- axis. Stanley Ocken Math 19500 Precalculus: Transformations of functions and graphs

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Transforming equations and graphs Transforming graphs of functions Sample problems Examples: Six function transformations There is a different way to change the equation y = x 2 . You can substitute an expression for the variable x. For example, if you substitute x + 2 for x in the equation y = x 2 , you get y = ( x + 2) 2 . The new graph will not be what you expect, and you have to be careful. If you: Effect on graph will be: Substitute x + 2 for x Move graph of y = x 2 LEFT 2 to get graph of y = ( x + 2) 2 . Substitute x - 2 for x Move graph of y = x 2 RIGHT 2 to get graph of y = ( x - 2) 2 . Substitute 2 x for x SHRINK graph of y = x 2 in x-direction by factor of 2 to get graph of y = (2 x ) 2 . In other words, divide every point’s x-coordinate by 2. Every point’s distance from the y-axis is cut in half. Substitute x/ 2 for x STRETCH graph of y = x 2 in x-direction by factor of 2 to get graph of y = ( x/ 2) 2 . In other words, multiply every point’s x-coordinate by 2. Every point’s distance from the y-axis is doubled. Substitute - x for x Reflect graph across y-axis. It’s natural to be puzzled by the above statements. Each change may be the opposite of what you expect. Nevertheless, they are correct. These transformations are shown on the following slide.

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